I almost always prepare my pasta sauce in the sauté pan where I’ve boiled dried pasta, using the low water method described here. I save a cup of the concentrated starchy cooking water to use in the sauce.
For example, slivers of garlic, halved cherry tomatoes, tomato paste, and crumbled dried oregano (I like the branch type I can buy at the Greek market) get a quick sauté in olive oil. Then the pasta—and enough cooking water to combine everything—get added back into the pan. I’ll add a dab more olive oil or butter at the end, off heat, to enrich. Variations using this technique are pretty much endless.
When I do cook fresh pasta, I go back to the traditional method of lots of water brought to the boil.