I learned by watching a tutorial Aine2 posted.
You have to make sure the gumpaste is rolled very thin. ( i found either gumpaste or 50/50 fondant mix works better then just fondant, or even MMF) After I press down, I turn the tappit over and score the outline of the letter. This not only makes a clean outline, but IMO makes it easier to come out. Make sure you dust the surface generously and then use the tappits exactly like it sounds....and tap it. Literally Bend it up in your hand and let it slam on the counter. Hopefully it will work the first time, if not just tap it again.
They really are a PITA in the beginning, so be patient and give it a few tries.
If you get too frustrated, invest in Clickstix ( sp?) I got them as a gift and not only is the font really cute and funky they're very easy to use. You start the same way as a tappit, but instead of tapping it, theres a little 'lever' on the back. When you push that, it pushes the whole letter out.