The first tool that I used was a scrub plane. This is a Western style plane and it is intended to be pushed, however, I sometimes plane by pulling it towards me, much like a Japanese plane. Using this motion I removed the high areas on the top's bottom.
The plane I own is made by Veritas. I really like "plowing" with it. It has quite a thick blade which eliminates chatter and makes sharpening easier.
I routinely checked the progression of my work with a straightedge. Once most of the surface had been trued, I flipped the board over and planed its upper side.