I just got this jeep at it was doing this to the guy that had it before me. I put in a fuse the day I got it and it worked fine for a day, but now its blowing out again. When the light were working they all worked correctly. Except the lights under the dash were burnt out.
Well, you definitely bought someone elses problems, but that's okay. Troubleshooting the electrical system isn't all too hard, it is just a very time consuming process. My recommendation is to get an electricl meter and a Haynes or Chiltons repair manual for the wiring diagrams. Some can also be downloaded (google it):
Google Search for 96 Jeep Grand Cherokee Wiring Diagram
The lights under the dash were out and everything else was okay? Check the mount and wiring for those and tape up any exposed wiring or solder that may be contacting ground. If that doesn't solve the problem just leave those bulbs out. If the fuse still goes, then you can...
Option 1: I'd start simple, pull all the bulbs and install them one at a time until the fuse goes poof. Then remove that bulb (and leave it out), replace the fuse, use the meter to check that socket. Continue on with the others to see if the fuse goes again. Repeat the process and note each bulb that causes the fuse to blow. This process can eliminate or locate sockets that are a problem, but not always. I've seen people push so hard installing a bulb that they bend the mount and ground it to the frame/body, so this is not a bad place to start. Also, I just feel that the bulbs are easier to get to compared to tracing wiring.
Option 2: Since wiring is hard to get to, try reaching in a feeling all the wires. Anywhere the wires come near a screw, mounting point, or bend, feel the wires for chaffing, cuts, or cracks in the insulation. Any exposed wiring that you come across should be visually inspected; find what caused it and fix that. Then wrap with electrical tape and test the system. You may have to continue on if the fuse goes again, because the problem can be at several points.
Option 3: Use the the meter to check all the components and switches connected to the problem fuse. You're checking for voltage and continuity. With luck, you'll narrow down the problem there. If not, you'll need to trace the wiring from the problem fuse, to each of the components connected to it, through any switches/connections, and then all the way to the battery, checking each section visually and with the meter as you go. The process involves removing several trim panels and IMO really sucks. You're looking at a hours of work.
Option 4: Take it to a shop and pay for 1-??? hours of labor. Shop around. Get a written estimates. It can get very expensive, so maybe invest in some flashlights until you can fix it yourself.
I highly recommend getting a repair manual simply because you sound like a DIY person. The manual will help you solve just about all problems.