I like the thinner shoots of asparagus - about as big around as your fingers. Just cut off the ends - about 1-2 inches. Then cut into 2-3 inch pieces and place the asparagus into a steamer basket with the thicker pieces on the bottom and the tips on the top. Steam over boiling water for 5-10 mins or until as done as you'd like. Then you can toss it with balsamic vinegar or just salt and pepper with a little lemon juice and butter buds. I sometimes make a ff cheese sauce to pour over it, too.
Just a word on "doneness." I grew up eating asparagus that my dear mom cooked in her pressure cooker - and she cooked it until it was mushy - now some people like it that way - but I since have learned to really like it with still a little crunch to it - so experiment and see what you like.