The key thing to remember when attempting to finely chop your vegetables is that each finger has a designated role.
Place your thumb at one end of the vegetable and your little (pinky) finger on the other end to hold the vegetable in place.
Use your ring finger and your index finger to hold the vegetable down.
Your middle finger should also be used to hold the vegetable down but it should play the crucial role of guiding your chopping hand as the blade gradually works its way through your vegetable. The middle finger also acts as a buffer to make sure your blade doesn’t cut too much at a time. Having said that, remember to cut very slowly and carefully to avoid cutting yourself.
For ease and smoothness of chopping, a very sharp knife is recommended.