During my last ride, my front derailer cable gave up on me and froze. I use this all the time on rides so I was thankful that it waited until we neared the end of our third day of riding. Here are the steps to change a cable on a bicycle. Each bike manufacture is going to be a little different, but these should provide you some guidance in general. Worst case you have to take your bike to a bike shop and pay for the repair, so go for it!
Step 1: Replacement Cable
Locate the correct cable for your bike. Stores like Wal-Mart and KMart often times have universal cable kits which ended up working great for my particular bicycle.