Before we get started consider where in the case you want the hard drive. Keep in mind that hard drives generate heat simply by operating normally. Something spinning at 7200 RPM is going to get warm. It is better to place them away from other hardware components as much as the physical constraints of the case will allow. If you want additional piece of mind then consider installing a drive cooler. And NEVER install the hard drive near the power supply. The power supply acts like a magnet and you know what magnets can do to data storage devices.
With that in mind let us proceed:
Slide the hard drive into an available drive rail of the case. All cases have a space or two for a hard drive that is below the floppy drive bay and has no access from the front of the case. Screw the drive into place, making sure not to force anything. The power connectors face the back or accessible side.
In some older cases, tightening down screws on the far side of the hard drive can be a problem, because the screws are not highly visible and thus it is hard to get to them with a screwdriver. It can test your patience to get at them. It is a major pain but doable. Today's newer cases have removable sides that make installation a snap.
Repeat these steps for any additional drives you might be installing.
If you are opting for a SATA drive, then things have just gotten easier.
Connecting SATA drives is easier as each drive connects to the motherboard using an individual cable; the host PC treats all drives as master devices, eliminating the jumper settings, which have frustrated users for years. This greatly eases installation and configuration.
SATA is software-compatible with ATA, so you do not need any special drivers or OS upgrades to support the new drives; the SATA controller does the conversion between the drive and host PC. This also means that SATA drives can coexist on the same system with parallel ATA devices.
The physical installation of SATA drives differs from case to case. With some cases, the drive rack is simply part of the case. With this setup, you simply push the drive into the case and screw it in. In other cases, the drive rack may be removable. Some have many separate racks, and some have one removable rack that can hold many drives. With this setup, remove the drive rack. This is usually done by squeezing two metal tabs together to release it, or you might need to use a screwdriver. Then slide the rack out. Screw the drive into the rack per above. Then, slide the rack back into place where it was.
When you are done, you should have a hard drive properly screwed into the case and the ribbon cable attaching it to the IDE controller and the power cable attached. At this point you are ready to move on to the next step in building your own PC.