1) We'll start by unpacking your case, PSU, and motherboard. Go ahead and install your PSU. Screws should come with your case and should be as simple as lining up the four screw holes and screwing it into place.
Your case should also come with some brass risers. They should screw into your case and will hold up your motherboard. There will probably be way more holes in the case than what your motherboard has. Just line up your motherboard with the case and add only the correct number of risers. Be sure you got them all correct or you could have one expensive BBQ on your first power up test.
Next take the IO shield (the metal plate with the holes for the back of the PC) from your motherboard box and pop it into your case from the inside.
Now carefully take your motherboard and install it into your case (NOTE: If you bought a special CPU cooling solution that requires special hardware you may need to skip to step 2). Start by pushing everything through the IO shield first. The shield often has metal tabs that are in the way. Feel free to gently bend them up and out of the way to make installation easier. Make sure you didn't get any stuck in the USB sockets or they could be permanently damaged. Now screw down your motherboard and then you're ready for step 2.
2) For step two we'll need your CPU and heatsink. To install the CPU unlock/open the CPU socket with the little arm. Align the CPU by matching the triangles found on the outer corners and drop it into place. The CPU will only fit in one way and no force should be necessary. While holding the CPU down move the arm back to the lock position.
Before installing the heatsink I like to take a clean lint-free cloth and use rubbing alcohol to clean the the top of the CPU. This insures that no oils or dirt from your hand are present which impacts cooling performance. Now apply thermal paste if required and install the heatsink according to the instruction manual that came with it. The heatsink should be firmly attached to the CPU. If it's loose or sitting at an angle you need to try again.
Finally remember to plug in the heatsinks's fan or the CPU will overheat. There should be a connector on the motherboard nearby labeled 'CPU fan'.
3) Next we'll install the RAM. If you have a dual channel memory supported motherboard, the slots are usually colored according to channel. Begin by pushing the plastic tabs on each side of the slot outward. Then align the RAM so the gaps in the stick match the peg on the memory slot, it will only go in one way. Press firmly and evenly on both sides of the stick until the tabs on each side close and lock the RAM into place.
4) Before things get too crowded we need to hookup your case to the motherboard. Look in your motherboard manual and hookup the switches, LEDs, fans, and USB/Firewire/sound. It doesn't matter which way the power and reset buttons connectors are plugged in and if you don't know which way the LEDs go then just guess and if they don't light up when you turn it on then just reverse them later. The other connectors should have slots and will only go one way.
5) Next we'll install your drives. If your case came with drive rails get them out and attach them to your optical drive(s) and/or hard drive(s). On some cases you have have to pop off the front cover to install the optical drives before sliding them in from the front. The hard drives will usually install from the inside. If you don't have drive rails then simply slide the drives in and secure them with the supplied screws.
If your drives are SATA then you'll use the SATA power connector and SATA cables. Otherwise you'll need the regular molex power connectors and the IDE ribbon cables. IDE drives my also require you to change the jumper on the drive for it to work correctly. Usually they ship set for Cable Select (CS) and will attempt to auto configure. A few SATA drives also have a jumper that changes it from SATA I to SATA II so make sure it's set correctly.
Motherboards often come with 4 to 8 SATA connectors and should be numbered if you look close enough. While it shouldn't matter what ports you use I like to use the first pair (1 & 2) for hard drives and next pair for optical drives. For IDE use the primary connector, often colored blue, then the secondary connector if you need it.
6) Finally we'll install the expansion cards. The video card will go in the top PCI-e slot and any other cards will go in the other PCI or PCI-e slots. PCI and PCI-e slots are not compatible with each other however you can plug in a smaller PCI-e (1x) card into a bigger slot (16x). If you have more than one open spot for a card it really doesn't matter which you choose, although many professional builders like to balance IRQs. Usually two slots will share the same IRQ which can be found in the motherboard manual. Install the cards so that they share as few IRQs as possible.
Installation is usually pretty simple. Remove the plate covering the slot on the back of the case that you want to use by either unscrewing it or unlocking it if you have a tool-less case. Then lineup and firmly press the card into the socket. Make sure the card fits all the way into the socket and isn't crooked. Some motherboards have locking AGP or PCI-e 16x slots that you can use to secure your hefty video card. Also many higher end video cards require a secondary power source to run correctly and will usually have a PCI-e power socket that must be plugged in.