The rim joist is the area just above a basement wall. Before insulating this area you will want to make sure there is no visual water damage or water stains. A sign of damage or stains could be a sign that the ground around the house is not sloped correctly or that you have a leaky gutter. You will need to correct the water damage and or water problem before insulating the rim joist.
If you find that your rim joists are dry then you can start insulating with a fiberglass or rigid foam board. What I have seen work good is a rigid foam board as the first layer and then a fiberglass batt (vapor barrier inward). This insulation will help keep your basement warm in the winter and cool in the summer.
If you have any questions just post your questions in this forum.