Well, you're not really supposed to be able to touch both feet to the ground at once, if that's what you mean. If you can put both feet down at the same time (while your butt is still on the seat), your saddle is way too low -- not only will you have trouble finding a comfortable balance on it, as you mentioned, but you'll have to work a lot harder to pedal, and you'll be in danger of damaging your knees.

A good first approximation to a comfortable seat height is that when you pedal, your knee should be very nearly straight (but not perfectly straight) at the bottom of each pedal stroke.

If you've got a trusted local bike store (or a friend who rides a lot), you might have them evaluate your bike's fit. If not, we can give you lots of advice, but these things are easier to explain in person, with the bike right there, than in writing...