Fixing deadbolts is actually one of the easiest things you can do. The only complicated thing is if you are replacing a really old deadbolt with the smaller diameter with a new deadbolt and a larger diameter. I ran into this with the front door of one of my rental units, and I had to drill the hole out. Luckily, there are templates you can be, attach to the door, then just drill through the template, quick and easy. With my fully-charged 18V RYOBI cordless drill, this took absolutely no time at all (and, I got the added benefit of being called handy, which is something I never thought I'd hear). So, on to fixing a standard deadbolt.
At my other house, there are several storage areas in the basement. I told the tenants that they could use them and lock them, if they want. Well, the tenant on the second floor wanted to use it, but there was no key for the existing deadbolt. Doh! In this case, I had two options, either take the deadbolt off, remove the cylinder and have it rekeyed, or just buy a new deadbolt and install it, keeping the old one for later use (after rekeying). I went with the format option, as that was the quickest (my local locksmith wasn't open at the time). Off to Home Depot to purchase it. These aren't expensive, maybe around $10, or so.
In any case, what makes deadbolts so easy to replace is that it usually consists of just unscrewing all the screws you can find, wait for it to all fall apart, then put the new one in and screw all the screws you can find. :) Let's take this step by step, though. The major screws that you'll need to unscrew are on the inside side of the door and, depending on whether you have a double keyed entry or a latch, the screws are either right on the cylinder or behind the latch. Here's a picture of mine, which was a latch-based lock. If you look closely, you can see the screws underneath the latch.

Well, there are two screws, and, after you unscrew them and take the cylinder off, you can (although not totally necessary) take off the bolt, itself. If you look in the picture above, you can see that the plate on the edge of the door has two screws as well. Unscrew those, take out the bolt and you'll have the following parts.

Putting the new deadbolt in is as easy as doing the above steps in reverse order. Put the bolt and faceplate back on the edge of the door.

Then, put the cylinder back on through the hold in the bolt and screw all the screws back together. Presto!! It should look like this.

Like I said, this is about the easiest task there is. I've done a bunch of them now, and I'm always amazed by the fact that people sometimes pay locksmiths to do this for them. All you need is a screwdriver, and a new lock is yours!