Ed's question was a little more specific, he bought a new hard drive to go into one of his removable trays and wanted to know how to install it. I decided to make the answer a little more generic to so that more people could gain from it.

1. <<Skip this step if you have a system like Ed's with removable drive trays.>>
If you plan on installing an additional drive in your computer, the first thing you need to do is make sure that you have a connection and a mounting place for it. Remove the case cover. 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.
SATA drive connections go straight to the motherboard. Just make sure you have a connection available.
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 unsafe 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!
If you have a place to mount a drive, but you don't have a place to connect it, you can install a plugin drive interface card. I won't cover that here though.
See RELATED LINKS below for nice pictures.
If you have trouble getting this far, you probably should call for help.

2. The next step is to set the drive jumpers.
SATA drives DO NOT use jumpers.
IDE drives (also known as PATA - Parallel ATA drives) have jumpers that have to be set for them to work properly. The average computer has two IDE connectors known as the Primary and the Secondary IDE interfaces. Each interface is capable of handling 2 drives. The drive furthest from the motherboard is known as the Master Drive and the drive on the connector closest to the motherboard is known as the Secondary Drive. Although these designations do not mean as much as they used to, we still must make sure that they are set up properly for the computer to function properly.
The simplest method is to set the jumpers to CS (cable select) and the drive's position on the IDE cable will determine how it will work. This is how most computers and drives arrive from the factory. Personally, I do not trust the CS setting and prefer to use the Master and Slave settings.
If you are using removable drive trays and everything is functioning properly already with a drive in the position that you are getting ready to install the new drive into, then just make sure that the jumper on the new drive matches the jumper setting on the existing drive.
If I set your machine up, then most likely all of your removable drives are set to be Slave drives. CD Writers work better if they are the Master drives so I usually set up a system with the hard drives as slave drives and the CD drives as masters. This allows you to move trays from position to position without haveing to worry about the jumpers or the flakey CS jumper setting.
If you are doing this all from scratch, then you will need to check the jumper settings on your other drives and act accordingly.

3. Now you need to prepare your drive for use.
If you are you are cloning your system drive or your data drive, boot your computer to your favorite clone software and go to it. Disk cloning software is a wonderful BUT unforgiving tool. BE CAREFUL, if you clone the new drive to your existing drive you will end up with two blank drives and loose everything.
If you are installing a new system drive, boot to the system installtion CD and install your operating system. The drive will be formatted as required.
If you are simply installing a secondary drive, boot into Windows. In Windows 2000 and XP, your new drive will not appear at all in My Computer until you format it. In Windows 9x/ME, it will appear, but you will need to right-click on the new drive and choose "Format" from the menu.
To format the drive in Windows 2000 or XP, right-click on My Computer and go to "Manage". In the window that comes up, click Disk Management in the left pane. Once it loads, you should see an "Initialize Disk" wizard pop up. Partition and format the disk to your liking, but make sure not to convert it to a dynamic disk, as doing so will provide plenty of annoyances down the road.
If for some reason you cannot find the drive, reboot the machine and go into the BIOS. Check the drive settings to make sure that all drives are being detected properly.

RELATED LINK: Drive Installation 1.

RELATED LINK: Drive Installation 2.

RELATED LINK: Drive Installation 3.

RELATED LINK: Drive Installation 4.

RELATED LINK: SATA Drives.