The only two ways I've found is beak color and singing.  The male zebra finch will have a very red beak, and females usually have an orange colored beak.  However, some females do have darker beaks, too.  Sometimes it's hard to tell without another bird to compare it to.  Singing is the only other way I've been able to tell.  If you hear one of them making these little beeps that sound like music, it's almost 100% guaranteed it will be male. 

Watcher in the Void, what are some of those white zebra finch behavioral problems, and why/how do they affect the ability of the birds to distinguish the sex of another white one?

Goodbird, this is what my zebra finch book has to say about the differences in white (true white) finches:

 

  Compared with the normal mating ritual, the courtship behavior of white zebra finches exhibits some serious disturbances.  A normally colored male suppresses the flight instinct of the hen by flashing his bright colors at her.  However, in the case of white zebra finches, the female immediately flees from the courting male, thus stimulating his aggressive drive so that he either chases her away or rapes her. 

 

  The immediate cause of this atypical behavior is not the lack of colorful plumage but rather the early imprinting caused by the presence of both white parents and white siblings.  Thus, white females raised by white parents do not even recognize colored males as members of the species and, consequently, flee from them.  They do ultimately get personally acquanted with white males and learn to appreciate them.  White males court white hens but will simultaneously chase away or even attack potential mates that are gray, something a gray imprinted male would never do.