Measure all three pieces of furniture as well as the dimensions of the room. Measure the unobstructed length of each wall and the width and length of the room. You can also draw the room to scale on a sheet of paper and cut out pieces of furniture to the same scale. This allows you to try different arrangements before moving furniture around.
Place the couch first. This is the largest piece, and it will likely be the centerpiece of the entire room. It should face the center of the room, as well as the front door.
Put the chair near the couch, preferably either across from the couch or at an angle, so that guests can converse easily.
Find a location for the desk that is away from the other pieces but adds to the ambiance of the room. Face it toward a wall or window to allow you to concentrate when using it for work.