Assuming you're using wood, not plywood or MDF or another engineered product, you'd use a high quality hand plane sharpened to perfection. Hint: if you bought your hand plane at Home Depot, Lowe's, or Sears it's a piece crap; throw it in the garbage so you won't be tempted to use it! If you've got a nice Lie-Nielsen, Lee Valley/Veritas, or vintage Stanley you're good to go! A block plane would probably be ideal, but you might be able to make do with one of the smaller bench planes (e.g. #1 or #2).
Mark layout lines on both edges of the piece. Set the plane to take a shallow cut. Start near the corner where you'll need to remove the most material and take a short cut. Do this 2-4 times, then move back a bit and take another cut. The idea is to gradually move the plane back toward the shallowest area to be cut. A good plane should be capable of taking paper-thin shavings off the wood at each cut. Pare down to the point where you just touch the layout lines. If you've held the plane steady, you should have a flat cut from one line to the other. if the cut isn't quite flat, you can clean it up with sand paper or a well-sharpened chisel.
If the cuts aren't wide, you might be able to do the entire thing with a chisel. You'd, essentially, use it just like the hand plane: take light, paring cuts until you'd trimmed the wood down to your layout lines.
That said, a belt sander isn't a terrible way to go. My Bosch 1274DVS has a flat top, so you can lay it upside-down on a bench bring the work down to it from above. Of course, the sander needs to be clamped in place and you need to be very careful when holding the piece!