Step 1:

Buy Equipment

Motherboard:

This is the main piece of the computer (also called a main board. This should be the first component acquired.
Make sure that it is the size you want. Make sure it has all the expansion slots you want.

Processor:

This piece of hardware is about 1 square inch. There are 2 major chips: Intel and AMD. I usually go with Intel if at all possible. The current processor is the Pentium IV. There are different sockets (configuration of pins) such as 478 and 423 and the like that need to match the motherboard. Otherwise, an adapter will be necessary.

Memory (RAM):

This is what programs use to execute. The amount of memory is usually a base 2 number such as 128, 512, and the like. It comes in megabytes(MB) now. The minimum I would recommend is 512 MB. There are different speeds and number of pins on the modules. Some have the classification of PC2700 333MHz 512MB 184-pin DIMM and such.

Hard Drive:

This is the unit where everything is stored. It usually comes in capacities such as 40GB, 80GB, 250GB, and so on. There are various speeds for these, but standard is Ultra EIDE ATA 100. Serial ATA and SCSI are other types of connections with other speeds. Be sure to get something that your motherboard can handle, recognize, and have the right connections.

Optical Drives:

A DVD-RW or CD-RW drive is great for burning DVDs and CDs. Most computers come with at least a CD-RW drive. Personally, I recommend having both installed due to speed issues. Most drives have IDE connections while others have SATA, SCSI, and the like.

Floppy Drive:

A 3.5" drive is not necessary, but could be helpful on occasion. This has a FDD connection.

Zip Drive:

Zip disks are becoming rare, but some older computers have them. They have been replaced by USB Flash drives. This fits in a 3.5" bay and usually is IDE.

Video Card:

This is not always necessary to purchase because it comes standard on many motherboards. However, the preinstalled version does not usually have much memory. The current standard is 64MB. Most newer motherboards have 4x/8x AGP, but others may not even have AGP. Only video cards fit AGP slots, but PCI video cards are options as well. The main thing to consider when purchasing a video card is the slot type and memory. Get more memory and 3D technology if you plan on playing games. If not, it's not necessary to have more memory.

Network Card:

This is usually on the motherboard, but if not, a PCI card would be nice. This allows the computer to connect to routers and other computers (more things, too). The standard speed is 10/100 MBps. A cheap, generic card can be about $3, but better ones cost as much as $30. There are USB network adapters available as well.

USB 2.0 Card:

This is useful if the motherboard does not have on-board USB 2.0. It is usually a PCI card.

Case (Tower):

This is what will be seen. Get a tower that is the same form factor as your motherboard. Get one that has as many 5.25" and 3.5" bays as you want and can support all of the PCI cards and AGP card you have. I prefer to get one with USB ports on the front to hook-up to the motherboard. I prefer to get a case that comes with a 400W power supply included.

Fans:

The more fans the better. There should be a heatsink and fan for the CPU. Also, there should be a fan that comes with the power supply. There might be a fan included with the case, but not usually. If the computer will be on for more than 2 hours at any time, have at least 2 case fans. Some cases can have as many as 8 case fans. Fans cost anywhere from $5 to $40. Some cases can have 2 in the front, some on the sides, and 2 to 4 on the back.