Dave, before you start. Are you using a piloted bit, one with a bearing on the bottom. You have to guide the router someway. You just can not hold it firmly enough without some kind of guide. The guide can be the piloted bit or a thick straight edge against the router baseplate. The torque and variations in the wood will just not allow you to hand hold the router weel enough without a guide. Remember, too, that you might not want to take off all the wood in one pass. 2 light cuts are better than one heavy one. And your real problems will be at the corners of the workpiece even with a pilot guide. If you are not very careful, you will tend to push the router around the corner of the workpiece. I really suggest that you try a couple of cuts on some scrap wood, just to get the feel, before you start on an expensive piece of wood. A router is not a difficult tool to use at all but, like every tool, some practice will give you a lot better idea what you are dealing with.
But in answer to your basic question, from the set-up you describe, you want to work right to left. Sears puts out a good book on the router (Item No. 29116) and you might want to check pages 21-25. This will give you some good info particularly on starting and ending a cut. Be sure to reread the safety rules and instructions that came with your router also.