How can I install a new lighting circuit in my kitchen?
You can in all likelihood run it off your existing circuit, but without knowing the current layout it is hard to say for sure.

You are probably better off hiring an electrician. Doing work like this requires significantly more information and technique than can be explained in a forum post or single diagram.

I am a firm believer in DIY, self-reliant amateur electricians, but just reading a few posts on a forum does not cut it. You need to have and use books that explain in detail the correct procedures, otherwise you could make serious errors with potentially dangerous ramifications.

If you have a specific problem, by all means bring it to the exchange, but just asking, "How do I wire up a whole circuit?" is not a good idea.