Materials -

Worsted weight cotton yarn. I used Brown Sheep "Cotton Fleece" and Lion "Cotton Ease" with good success.
Size "F" crochet hook
Yarn needle to weave in ends.

Notes -
A good photo of the single crochet stitch that I use can be found here

Some tutorials show a variation of the single crochet stitch splitting the top loops, I prefer to crochet into the "space" With the exception of round 6.

Photos of "crochet through the back loop" can be found here

Teacup Base-

To begin - Chain 4, join with sl stitch to first chain, making a ring.

Round 1- Ch1, (counts as first sc.) Sc 5 more times in ring. On this and all following rows, join to the top of first stitch of row with sl st to finish the row.

Round 2 - Ch 1, 1 sc in sl st space (counts as first 2 sc) 2 sc in each space to end of row, join.

Round 3 - Ch1, 1 sc in sl st space (counts as first 2 sc)* sc, 2 sc (in next space) repeat from *to end of round, join

Round 4 - Ch 1, I sc in sl st space,* sc, sc , 2 sc. Repeat from * to end of round, join

Round 5 - ch 1, sc in sl st space, *sc, sc ,sc, 2 sc Repeat from * to end of round, join.

Round 6 -ch 1, 1 sc through the back loop in each stitch. This will make a little horizontal ridge in your fabric that separates the base from the sides.

There will be a little bit of a "jog" at the end of this row that is about half a stitch high. I have no idea how to avoid this. I just made sure it was on the same side of the cup as the handle to be the least noticeable.

Teacup Sides -

Following rows - sc (no increases) around and around in a coil until your teacup is the desired height. The teacup width and height should be about the same. I just "eyeballed" mine until I was happy with the height.
When your teacup is the desired height, do one round of slip stitches through the back loop (one in each space). This gives you a nice finished edge.

After completing the last slip stitch, sc in the next space and then ch 8 st. This will become your handle. (You can make the length of the chain longer or shorter if you want to change the look of your handle)
Turn the cup sideways and sc one stitch through the side of the cup a few rows down from the top. (This stitch attaches the bottom of your handle to the cup)
Turn your work so you can prepare yourself to crochet back up the chain you just made.

Sc around the handle chain stitches until you reach the top of the cup. The number of stitches will vary depending upon your tension, but for a nice firm handle, I crocheted mine pretty tightly and close together.
When you get to the top of the teacup, break your yarn and leave a tail of about 8"

Using your yarn needle and the tail of the yarn, sew a stitch through the top stitch of the handle and through the body of the cup to make the handle extra secure.
Weave the yarn down through the inside body of the cup and make a stitch through the body of the cup and the bottom stitch of the handle. Tie off your yarn and weave your end in.
Use your preferred blocking method to shape the teacup. Voila, you're done!

To make a saucer for the teacup, crochet in the round and create a base as you did with the teacup, keep increasing every row until the diameter of your saucer is satisfactory. Crochet one or two rows with no increases to make the lip of the saucer.
Finish the saucer as you did the teacup with a slip stitch row for a finished edge. Tie off and weave in your ends.