Instructables
video How to cut an onion
It's dead-simple actually. Look and learn.

The short: Cut top and bottom, cut in half, remove skin with one extra layer(this is for easier removing), chopchop!
Make small slits first, if you want diced.

I can go on for hours about right cutting techniques, but it comes down to: Hold the knife in hand and insert knife in object to be cut. Sharp side first.

**Remember folks, knives love cutting fingers. Don't chopchop them up!**