It's very very easy, even for a novice.
The CD Drive in your PC is connected by 2 cables. One is a 4 pin Molex connector that provides power to the drive, the second is an IDE Data Cable that connects the Drive to the mother board.
Generally, the drive is held in by 8 screws, 4 on each side of the drive. The replacement is a simple procedure, you simply take the sides off the case, usually by removing a few screws on the back and sliding the sides toward the back of the case to remove them. You then remove the screws on both sides, and unplug the 2 cables. The new drive slides right in where the old one was, you put the screws back in, and connect the 2 cables the same way they came off the old drive. On 99% of all computers, this process is very simple and takes about 10-20 min even for people that haven't done it before. Make sure the computer is unplugged from the wall before you do this.
As for the replacement drive, there is no point just looking for a CD/DVD Player. Most drives on the market right now are also DVD Burners. There aren't very many read only drives left out there, but the burners are so cheap there is just no point in making anything else.
If you would like an example of a nice drive that would be dirt cheap try
this one from Newegg. It plays and burns both CD's and DVD's.