The process you've learned for taking a compass bearing from a map and following it is very reliable. Now that you know it though, we can move on to a shortcut that works especially well with thumb compasses.

Start by folding your map down to a size you can easily manage in one hand along with your compass on top.

Line your compass edge up with the direction you want to go on the map (just like in step 1). Now turn your body till the north lines on the map are aligned with the magnetic compass needle. That's it — you and your map are facing the direction you want to travel.