Note, this tutorial is for adding an additional hard drive to your current computer. For setting up a new hard drive, you will want to refer to HowTo Install Windows from scratch.
This tutorial assumes you are using IDE drives, although SCSI isn't much different except that instead of setting master and slave, you will need to set different IDs for each device, with the last device in the chain set to terminate.

Why?

As your computer ages, your hard drive will likely fill up with software and files.  If you're too lazy to clean it up and remove old programs or have already done that and need more space, a new hard drive can give you a lot of additional storage. You could also set up another hard drive for keeping a second OS on (like NT, Linux, etc.).  Setting up a second hard drive can also be beneficial if you choose to use it as your swap drive. A newer hard drive will likely be faster than your old one, so you may want to move all your software to the newer hard drive (thus, the newer hard drive would speed up your computer).

How?

1. Remove the case cover. Make sure you have room for another hard drive!  You need to have an extra connector on an IDE cable (or an extra connector on the motherboard for which you would need to get another IDE cable).  Just look in your case for the IDE cable(s) attached to your hard drive and CD-ROM drive. If there are extra connectors on the cable, you're in business. If there are no extra connectors, but there is another cable or a connection for another IDE cable (would need to be the same size and right next to the currently used IDE connector on the motherboard) then you are also okay but may need to get a new IDE cable.
Next, make sure you have a place where the hard drive can be installed! There should be a 3 1/2 inch bay for an extra hard drive (but not in all cases).  If not, you don't want to get a new hard drive because it is unsave to have it in your case not properly mounted.
Last, make sure that the cable will be able to reach where you plan on putting the hard drive! If it can't reach without some reorganization of the cables, there's not much you can do!

2. Provided you have room for the hard drive, check all your current IDE devices to see what the jumper settings are. Most IDE devices (Hard Drive, CD, etc.) will have jumpers that will match up to a description somewhere on the device of what those jumpers mean.  Your current hard drive should be set as master.  For each cable, if there are two devices on it, one should be Master, and one should be Slave according to the jumpers.  Keep this in mind when installing your new hard drive.  You will usually want your hard drive to be master unless there is another hard drive on the cable (then one must be master and the other slave)  i.e. if there is a CD-ROM drive on the cable you are putting it on, you will want to change the CD-ROM drive to slave and set the new hard drive as master.  You also want to have your boot hard drive as the Primary Master (one IDE connector is Primary, the other is Secondary, labeled on your motherboard).

3. Place the hard drive in a proper bay (preferably where it will receive good air flow to keep it cool).  You will want the silver side of the hard drive to be on top, and the connector facing towards the motherboard so that you can plug it in.  Find an extra power cord (from your power supply) and connect it to the hard drive (you can buy splitters if you don't have extra power connectors). Plug your IDE cable into the hard drive. Close up your case.

4. You will now want to go by the procedures in How To Install Windows from scratch for setting up the new hard drive with fdisk and format.  The only difference is that you won't want to set this partition active. 

5. If you wish to make this new hard drive your main hard drive (and boot to it), you will want to do two things.  First, get Norton Ghost and use it to clone your first hard drive to your new one (follow the instructions that come with the software). Second, put your new hard drive on the Primary Master IDE cable, and make sure it is set as Master.  Put your old hard drive where you had the new one, and make the master/slave setting the same as what the new hard drive had been. That's it!