Once you get used to strumming you may want to venture out into different techniques. There are quite a few techniques to just play specific strings on guitar, and it mainly depends on the sound you are going for. You can of course use your fingers, but for the sake of this blog post, we'll take a look using a pick to only have certain strings ring out. You may want to do this as a strumming or a soloing technique.
The first technique is to not strum certain strings and focus in on the exact string you want to pluck. The way to do this is to make sure you are strumming with your wrist and not your elbow. You will have much more control of where your pick is. The other trick is to always alternate between up and down pick strokes. This will help your timing. Start slowly with this technique and gradually work up speed. Use this technique if you want to create a nice picking pattern with chords
If you want to hit certain strings as you solo, the Stevie Ray Vaughn approach sounds great (especially for blues soloing). Here's how you do it. Use you index (pointer) finger to damp all of the strings. Now use your other fingers to hold down the note you want to hear. Strum all of the strings, and you will hear only that note with a heavy percussion sound behind it. You pointer finger should feel "dead" like a heavy weight. Over time, this technique will work its way into all of your soloing.