How to make a cappuccino not overflow?
Two suggestions, one practical, the other probably less so.

1) Hold the cup directly, instead of the plate the cup is on. I don't know if that's allowed by health code or restaurant policy, but if it is, you get much more stability from cupping the cup in your hand than balancing it on a small plate. If you're already doing that: practice will get you there.

2) A good cappuccino should be fairly stable. I know there's disagreement about the proper way of layering cappuccinos, but the best ones integrate very finely textured foam into the milk, instead of just layering coffee - milk - foam on top of each other. Milk foamed this way is more stable than regular milk; I've carried cups filled to the brim up the stairs without any spilling. But: this is a barista-side issue, and to be honest, I wouldn't touch it ... the barista is going to make the cappuccino how s/he feels it's best, and being told to do something differently won't go over well.