If you're using the router free-hand, you could clamp a straight edge under the piece, and set the router depth so that the bearing follows the straight edge. The straight edge will have to be something with a bit of thickness, like some aluminum box-tube, or perhaps an already straight edge of plywood or MDF.
If you've already got one straight edge, and you need the opposite edge to be parallel, that's best left to the table saw (until you've got a bit more experience with the router).
Perhaps you could post some pictures of your project along with a description of what you want to do? If we know what you're working towards or trying to make, I'm sure someone can offer better / more specific advice.