Building your computer from individual parts starts by getting a motherboard, CPU, RAM and hard drives.
The motherboard is the part of the computer that everything else connects to; the CPU is what actually makes your computer a computer, the RAM is where your computer does all its work, and the hard drives are where your data is stored. You'll also need a video card, and will want a network card (or wireless networking card), and may need a sound card if your motherboard doesn't have onboard sound. You'll also need a monitor, keyboard, and mouse, and you'll want a case to put it in and some fans. Let's assume you have all the parts, and were smart enough to do a bundle buy at a place like NewEgg.com, where someone else selected the CPU, RAM and motherboard so they'd all work together. (For computers that are "last generation" stuff, this is often a great way to get a really cheap computer for a tiny amount of money.)
OK, you're going to need a screwdriver, a well lit place, and a magnifying glass doesn't hurt. Following the instructions for your case and motherboard, mount the motherboard into the case. Plug in the leads from the power supply into the motherboard, and hook all the connectors up to the front plate and backplate. Power it up – there will be LEDs that should light up; if they don't, you may need to talk to whoever sold you the motherboard.
Now, power it down again. Put your CPU into the CPU socket; this can be tricky – but don't force it. Eventually, everything will line up and it'll pop in. Now, practice putting the heatsink / fan on the motherboard, then take it off, smear some of the thermal paste onto the top of the CPU, trying to make an even coat, and put the heatsink on. There will usually be a spring tension locking lever to hold it in; use it. The single largest cause of dead CPUs and motherboards is forcing the former into the motherboard and bending a pin, and trying to run it without the heat sink on it.
Once the CPU is put in, put the RAM into the slots, and plug in the hard drives. Make sure, when you buy the hard drives, that the use the same connectors that come with the motherboard (which is why we start from the motherboard and work our way out). SATA hard drives are faster, larger and easier to find than the older IDE ones. SATA versus IDE is a good reason to choose one hard drive over the other. Most hard drive bays have screw mounts so you can mount the hard drives in there. If your hard drives come with fans, make sure the fans are connected too. Hard drives can get pretty hot, and it's not good for them.
Now, put in the video card, hook up the monitor, and turn on the machine – you should get a "POST" test, identifying the CPU and how much RAM you have, and with luck, it'll tell you it's found the hard drives. If it hasn't, you probably need to look at the motherboard's manual again and play with some jumper switches.
Finally, plug in all the other components where they're supposed to go, including that CD-ROM Drive. You'll need the CD-ROM drive to install Windows or Ubuntu Linux. Leave the case open while you're installing the operating system, just in case something needs to be adjusted.
You're well on your way to building your own computer.