Here is another great example of what you can do with half square triangles. Sugar Bowl consists of squares and half square triangles.
Of course, the most important thing about half square triangles is squaring them up. That helps you get your points perfect. I say "helps" because sometimes no matter how hard you try, they are still not perfect. But that's okay.
I have been quilting for close to 30 years and after loosing my job twelve years ago, I am now able to do what I love, QUILT! I specialize in baby quilts and have designed the "Lovie Lap Quilt" with pockets.