I have an old poured concrete walkway that has some low spots. When it rains they fill in with water. How do I pour new concrete on the old and have it hold?

Well I waited for other answers here's mine,
I don't recommend pouring on top of existing concrete mainly because I've never seen it done on residential walks and driveways better to just break up the old and go with a new monolithic pour

This would not be a good fix. Bonding new to old is not as easy as you may think. You'd need to pour at least a 2" thick pour on the high spot and more on the low spot. To make it look right you'd need to do this the length of the walk. Either tear it out and pour a new walk or get some large pry bars and leverage the low spots up to grade.

Thanks for you quick answer... now were did I leave that sledge hammer... and who should I call over for a little mixing party and a couple of beers

Its too bad saw-cutting is so expensive and noisey and dirty but if you know someone with a machine you can either scour it so it will break in sizes you want or cut it into walking stones or whatever

Pouring over existing concrete will last... about a day. Do like Bal. says and tear it out, or try to level it, if you're lucky.
It's a lot easier to break up if you pry it up, get some air space underneath it , and THEN hit it with a sledge hammer. Get a keg of beer, and invite your friends over to see who can break it best. But be careful, and watch your eyes.

Are you good at finishing concrete?

Yes but better at finishing that brew