Think it's not possible?  Here's a successful method for doing just that.

Most dog owners probably know all the basics.  But maybe it's best to start with a description of proper heeling.  A dog who heels remains close to her owner's side at all times, while on a completely loose lead.  (A leash is irrelevant to a dog who heels.)  She immediately sits after her owner stops.  She never lunges at another dog or person or animal.  She doesn't pull.  She doesn't stop to urinate or defecate.  She doesn't try to smell trees or rubbish.  She doesn't reach out to sniff passersby.  If you understand that your dog is wholly allowed to smell things, meet other dogs and people, and urinate when she's in release mode but not while heeling, then you're on the right track.

Now, to start your first heeling training walk.

First, get out there on the streets with all the distractions.  Trust me.  Everything will move along faster that way.

Preferably, using a flat collar (but a nylon mesh slip collar is okay if you need the extra "umph") and a four to six food lead, start walking your dog from a sit, saying "heel" as you move off.  (If she doesn't immediately follow, a little coaxing as you continue walking away - never stop - should get her moving.  Try slapping your leg or jogging slowly to entice her.)  If absolutely necessary, a gentle tug and release will help.  ("tug" meaning 1/4 of a second of contact with her neck and immediate release for at least a second or two before the next tug, if necessary)

Never stop to look back at your dog if she's misbehaving.  Just keep moving forward.  You can quickly look back, but only if you're still walking forward.

Never, never, never keep a tight lead.  It should always be loose, completely loose, unless you are "correcting" her for a nanosecond.  Only hold the end of the leash. 

**A note about training equipment**

Any equipment you use on your dog (I.E. collars, leashes, halters, harnesses, etc.) are merely training tools.  They're there to keep your dog under control while it learns to obey verbal commands and control its own behaviour around distractions. 

Used responsibly, most training aids are effective.  However, they should not be seen as a solution for problem behaviour.  Head halters, choke chains, prong collars, even leashes, are merely a means of keeping the dog under your control while you continue training appropriate behaviour.  The goal is a dog who will be obedient without any equipment at all to guide her.  Relying on equipment to control the dog means she will never learn to control her own behaviour, and will always have a need for strict supervision and physical control.

Now, imagine an area to your left (assuming she's heeling on the left) that is about two feet wide and four feet long (two in front of your left arm and two behind).  Your job is to expect her to remain within that "batter's box" heeling area at all times, or until you give a release command like "okay" to allow her to stop heeling.  Always give a release command from a sit.

In my years of retraining dogs, I've found that it is always the owner who sabotages the training.  So read carefully.  On a heeling walk, she is to remain in the heeling position at all times.  If she starts to walk ahead or away from your imaginary box, simply say "heel" and turn either 90 or 180 degrees away from her.  Let HER run out of leash.  So, brace for the tug but don't stop walking.  Yes.  The first few times, she'll invariably whip around, then try to catch up with you.  Once she's back in the batter's box, praise her and say "heel", then praise again.  Continue in this direction for a little while.  Don't immediately turn back to the previous direction, if possible.  Perfect heeling-turns and an automatic sit will come later.  For now you're just concentrating on heeling while moving forward.

Re: when saying the word "heel", this is what you're aiming for:  You want to give the command, then wait a half second for a response from the dog.  If she doesn't, in fact, heel, then you have to do the "correction".  You're teaching her a cause and effect relationship between giving her a command, and expecting her to react.  If she doesn't "heel" as soon as you say so, she gets a little tug on her neck because you moved off in a different direction.  So, remember, it is the command FIRST, then the realization that she didn't do it, and the resulting consequences. 

1.   Command ("heel") 

2.   Did she do it?

3.   Correction (turn), if she didn't.

4.   Praise either if she did heel, or praise after correcting her and she is "forced" into the correct position. 

When she is in the heeling position she needs to know that everything is wonderful.  And, when she's not, it's uncomfortable.

Do the turning thing every time she ventures outside the heeling area.  I can't emphasize this enough!  Every time!  Yes, it's tiresome.  But don't 'not do it' because you don't want to look silly in front of the neighbours.  And don't 'not do it' because she sees another dog and is already pulling towards it.  She is not allowed out of that imaginary perimeter unless you say it is okay first.  As soon as she is outside the heeling area, say "heel" and do the turn.  When she catches up, say "heel" and praise, praise, praise.  In this sense, it might be best to plan your walks with limited distractions.  Real world, street walking, but maybe on quieter streets.

By the way, you don't have to yell your commands.  It almost works better to use a softer, but deliberate tone when you say "heel".  Just once.  And mean it.  Lovingly mean it.

If you come across another dog on your walk, act as though you see nothing.  Concentrate on what your dog is doing.  If she moves outside the box, do the turns.  It really doesn't matter to you why she is outside the box.  She is to remain in the heeling position, regardless of distractions.  That's actually how she learns to ignore distractions.  Practice. 

Don't start pulling the leash, etc.  A quick tug on her neck because you've moved off in the opposite direction is all you're looking for.  If you are moving away and she is adamantly still pulling in the opposite direction, and you have no turning option left, you may choose a quick, manual tug and release on her leash, as though you've chosen yet another new direction.  This is probably the only time I'd say give your dog a manual correction yourself, ...as opposed to her running out of leash 'cause she's not following you. 

(The biggest mistake most dog owners make is keeping a tight leash, where the dog is actually pulling the owner towards the distraction.  Once they both breathlessly arrive at the distraction, the owner gives up.  This does one thing.  It teaches the dog that physically pulling the owner is not only possible, but that it can get what it wants if it does this.)  Tug and release can keep a horse in line, why not a dog?  It is actually the constant pull that is ineffective.  Remember, tug and release.  It's kind of like pumping the breaks to avoid lock up.  If your dog tries vehemently to pull towards a distraction:  Tug and Release.

Yes, you'll feel like other dog owners are looking at you like you're nuts, zigzagging all over the place with your puppy just trying to meet another friendly dog.  If you call out "I'm working on heeling", the other dog owner will likely understand and move off with his/her dog, so they aren't a further distraction.  Once your dog is heeling, you will be walking right past other dogs, without incident.  If you do choose to meet another dog, ask your dog to sit and wait 'til you give a release command like "okay".  Then your dog will be free to meet the other dog.   If you don't teach a release command, you'll actually be teaching your dog to disobey your "heel" command.  A dog simply isn't allowed to meet another dog while heeling.

If your dog is treat motivated, you might want to carry some easily accessible treats, just to get her attention back on you if she is determined to get to another dog while you're trying to teach heeling.  While moving away from whatever direction she's going in, try to wave a treat in front of her nose and draw her attention in your direction.  If she does, say "heel" and give the treat instantly.  Continue your heeling walk.  If you're able, try the treat thing before you manually tug on her if she's really not paying attention.

I know.  I know.  This first walk is all about perseverance.  It probably won't be fun and you'll probably want to give up.  But trust me.  We're building on something here.  Do keep in mind all the praise.  Instantly praise when she's doing something you like.  And praise as a matter of course when she does remain inside the heeling perimeter without you having to remind her, no matter how short a time.  In all likelihood, you'll return home very tired (arms and voice) and maybe even a bit frustrated.  It's to be expected if this is your first, true, heeling walk.  If the second walk is similar, you may think you can't keep it up for another two or three walks.  But, stick with it.  It'll come.  I promise.  If you are consistent, and never, ever let her do anything on her own, I.E. without a command from you first, then she'll soon learn there is no option but to obey.

If she has been behaving for a short period during the walk, cut her some slack and praise in a really playful way.  Try to get her to jump or hop or something to release tension.  Then continue as usual.  If she falls behind, don't jerk her to catch up.  Try jogging and coaxing, slapping your leg and saying "heel".  Remember to smile.

When you get home, stop and ask her to sit.  Then give a release command like "okay", but keep her on the leash.  Play and have fun with her on the leash for a minute or two.  Let her urinate, if she needs to.  You're teaching her how to be in release mode while on-leash.  Then, ask her to sit again and remove the leash.  Make all the noise you want in removing the leash, but expect her to remain sitting 'til you give her the release command.  Only then can she run off and play and let off steam.  Be her playmate.

I walk my dogs about four or five times a day.  So, if you do this for the next three or four walks, you'll see a marked improvement in her comprehension of heeling.   In my experience, by this time tomorrow, you shouldn't have any real contact with her collar from now on.  The only exceptions should be minor corrections and probably major distractions like other dogs.  Although, depending on how consistent you are, you may even see significant improvement in this area too.  If you are consistent, it won't take long for her to be heeling like a pro, even around other dogs.

It is all about you.  If you expect her to walk right past distractions; if you expect her to remain heeling no matter what; if you expect her to heel and/or stay sitting until you give a release command, then you'll likely end up with a well-behaved dog in no time.  We all forget once in a while.  Just the other day I was coming in from a training walk with my dog.  I opened the door, took one step in, and stopped.  I was looking at some pamphlets or something near the mailbox.  My dog was half way through the door when she stopped, and looked up at me as if to ask 'What do you want me to do?'  She couldn't sit where she was.  It was her look that reminded me that she was supposed to be heeling, so I better move all the way through the doorway so she could sit.  I praised her for doing such a good job.

My own preference, after this first day of training walks, is to go on at least one heeling walk per day.  Meaning at least one walk per day is entirely heeling.  On other walks, I might use an extend-a-leash so she can move all around and sniff, etc.  She still has to heel when we come across a pedestrian or another dog or to cross a street.  But, once the distraction is passed during non-training walks, she is given a release command to go back to sniffing and roaming on a long lead.  I make sure she has at least one off-leash run in a park or woods per day, also.  No training, just running and playing.  Try to be your dog's playmate as much as you can.

Remember:  When she's heeling, she has to stay heeling.  If you want to let her sniff or roam or meet another dog, ask her to sit, then give her a release command BEFORE allowing any of these activities.

Inasmuch as it is possible on the first gruelling day, try to make it fun.  Be positive.  Laugh as much as you can.  Tell her you love her.  Tell her what a good girl she is.  Try to have age and experience appropriate expectations of her.  The first day, if you can just see that she's no longer pulling, I'd think that to be excellent progress.  If you're anything like me, you'll probably have to fake your "happy praise voice" for the first few walks.  The first walk or two is just letting her know there is no option.  The second or third walk is about a more precise understanding of the expected behaviour.  And walks four and five reinforce to the dog that she is doing what you want.  From that point on, it is simply perfecting the behaviour and reinforcement.