I didn't use to really like vegetables. I guess I wasn't that unusual for being a kid, but point being that veggies weren't my favorite and I only liked them certain ways. I didn't like them raw, I didn't' really like them fried, I'd never tried tempura; however, I did love my vegetables steamed. Now granted, my range of likable veggies wasn't very big, but the ones I did like, I liked best steamed. Steamed vegetables aren't hard to achieve and they are one way that I've found almost everyone likes their vegetables.
Whenever you steam your vegetables, you'll want to cut the veggies up into smaller pieces. Some vegetables come precut like that (most frozen vegetables do), but at least some of the time you'll need to do your own cutting. You don't want the pieces too big and you can basically go as small as you want. I try and make my broccoli pieces small enough for bite-size or enough for two bites and my carrots about the same. You can get away with really small pieces, but too large pieces are hard to handle and don't usually cook as well. Once you have the vegetables cut, you can begin the steaming.
Fill a medium sized pot with some water. You don't want the water to completely cover the vegetables, but you do want to put enough water in so the steam from the water can actually cook your vegetables. A good rule of thumb to follow is to fill the water up so it covers about three-fourths of the vegetables in the pot. Add some salt to the water and then put on a burner turned to high. Put the lid on so the water will heat up faster (but you don't want the water to overflow so be careful).
Once the water starts to boil turn the burner down to about medium-high and let simmer for a good fifteen or twenty minutes. Periodically check the vegetables' tenderness; this can be done just with a fork. Once the tenderness is to your liking, the vegetables are done and you can sit down and eat! Steamed vegetables often taste good with extra salt and butter.