Another trick for finding leaks that I don't see mentioned here is soapy water. Pull the tube out, and make a preparation of very soapy water. I particularly like dish detergent (e.g. dawn) because it is so concentrated, but any soap should work. When you brush soapy water over the tube, the air escaping from any leaks will form soap bubbles. If you don't have a great place to submerge it, this trick can be a lifesaver.
When you're looking for a slow leak, you want to find the cause of the leak. To do this, it's important to mark the tire, the wheel, and the tube in some way so you can figure out exactly where the hole came from. You can use the valve stem on the tube and the rim to figure out where they fit together, but you should mark the tire to indicate where the tire sits in relation to the valve stem. If you do this, and keep them oriented the same (i.e. don't flip them over as you work on them), you should be able to find the leak and to find the place in the rim and the tire that's near the leak.
Once you find the spot, inspect the rim and the tire. Any problems with the rim should be fairly obvious if you run your finger over them; check it and move on to the tire if you don't find anything. When you are inspecting the tire, start by running your finger over the offending surface. If you feel something sharp, be sure to dig it out. If that doesn't work (and with a really slow leak, it often won't), you'll need to get more aggressive. Turn the tire inside out, and fold it over in that area. The fold should stretch the inner rubber wall, and any holes caused by punctures will be more obvious. Find the hole, and then dig around in the hole with a small screwdriver or something. I've often found little shards of glass or bits of wire embedded in the tire itself. You can't feel it, you can't see it, but it can still puncture your tube when you go over a bump just wrong.