How do you cook flavored pasta?
You cook it the same way as you cook "regular" pasta.

As for the sauces, try to keep it related to the flavor of the pasta.

Squid ink pasta should be used with seafood sauces (vongole...)

For tomato pasta or spinach pasta, I tend to keep the sauce as light as possible; just olive oil, garlic, little bit of herb as to not hide the pasta colors; no cream sauce, no full-on tomato sauce or ragu sauce.