I'm trying to fix up an old guitar and when i plugged the cable into the jack there wasn't a signal getting to the amp. I unscrewed the jack and found the reason for this was an exposed portion of the wire was touching the input, stopping the signal. Any suggestions on how to fix this?
Either resoder a new set of output wires to the jack or just try to cover the current exposed wires with electrical tape.
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It's probably an easy fix, but if you aren't sure what you're doing you should probably get someone to do it for you.

I recently had the jack replaced on one of my guitars, it only cost me £15 including parts & labour. That's a far better deal than attempting to do something yourself then causing more damage and having to have someone fix that as well.
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It's pretty hard to cause more damage. Does the wire run directly to a pickup? What is the configuration? Learning to solder can be rewarding in the sense that you're fixing your own gear, and you're also learning how the guitar works. Guitar Electronics for Musicians is a great book to learn all of the various circuits.
I know the problem is that the wire is stripped and the person who wired it soldered the wire to the inside of the jack instead of the outside. I know how to solder but I was just exploring my options before I have to do that.
just cut off the bit of wire that's loose, assuming it's excess from what's attached to the jack.

seems like a fairly obvious solution