I want to add 2 new lights to an existing light in my kitchen ceiling. What kind of wire do I use and how do I connect them? Hook black to black, white to white?

NM-B or what's called Romex. Use the same wire gauge as the existing wire which will be 12/2 or 14/2. Ground is automatically assumed.

Depending on where you splice in, you will be connecting at the black and white from an existing light. Use a wirenut appropriate for the number of wires and the wire gage.

The ground needs to go the fixture and the metal box if used.