for sauteing, i use just enough fat to let the veggies move in the pan and cook on high heat. this is probably the fasted process because they should still be crisp when you're ready to eat them, but still tender enough to eat with a fork. if i want to add some extra fat for flavor, i'll throw in a little butter just a bit before they're ready to come off the heat.
for grilling, i tend to use even less fat because i don't want too much flame coming up and scorching them. i still cook on pretty high heat there, and brush on a little olive oil just to keep them from sticking to the grill, grill pan, or each other. i keep a pretty good eye on them (unless it's something wrapped in foil, like an onion) to catch that just crisp enough done-ness.
roasting is the thing that takes some experimentation or looking up cooking times. most veggies can be tossed with oil and seasoning and baked at 350 for 45-60 minutes and come out tasting pretty great. but i prefer broccoli and cauliflower at 425 for 20 minutes, brussells sprouts at 400 for 40, etc.
roasting is also where i use the most fat, which is party why it tastes so amazing, but i don't really measure. i do like the veggies to be fairly well covered in it though.