Here is a video clip showing how to use a hand plane to even up individual planks of a table top and also to flatten it across it's width.
This is one of the techniques that goes into a hand made table. Working with a sharp plane like this is a lot of fun. It is very satisfying as it hisses through the wood. This will be one of my Trestle Tables but with have two add-on end leaves. I will post more about this table as it comes along.