I am horrible with knives. Being accident prone definitely does not help. After hours of watching Food Network, I now feel like I know the correct way to hold a knife and to chop things. Unfortunately, I still somehow never seem to do it correctly. I doubt I'm alone.
One of the most important things to remember when beginning down the path to better knife skills is the "claw" technique. This technique involves holding your hand in the shape of a claw over the vegetable (onion, let's say) so that if the knife slips, it hits your hard fingernails and you keep your fingers in tact. I'm getting much better at "the claw", so I'm happy to let you know that my fingers are doing well.
Practice makes perfect, so my early New Year's Resolution is to master the art of chopping and dicing by practicing my knife skills daily. There are a ton of videos you can watch online to help you figure out how to hold a knife and make sure you're cutting evenly. Here is one I think does a really good job.
Stay safe and good luck!