NOTE: This assumes you have a new case with nothing in it... if you don't, there's more steps involved, namely, disconnecting all the cables/wires from the old motherboard, removing the motherboard from the case, and detaching it from the metal tray/sheet. Please be sure you ground yourself first (see below)
Here's the order I put things together and the precautions I take:
If your case has a removable motherboard tray, slide it out first. If not, remove the metal sheet that attaches to the case so you can mount the motherboard to it.
Set your tray/sheet down on a flat, non-static area (wood or rubber are best) and make sure you ground yourself also. All I mean when I say ground yourself is make sure you're not going to get any static electricity "pop" when you touch any of your computer components (especially the motherboard/CPU/RAM/add-in cards). Use common sense, ie, don't go doing this on a thick carpet while wearing socks. Also, try to handle the components by the edges only.
Figure out where the holes of the motherboard line up against the tray and attach the standoffs (metal screws with an allan wrench head) to the tray. Now set the motherboard down on the standoffs and mount it to the tray. Don't get carried away tightening the screws you use to mount the motherboard to the tray. It should be tight, but no more.
Once you've done this, put your CPU in the socket and lock it down. Try not to touch any of the pins on the bottom of the CPU as you do this. This limits the chance of any static electricity shorting it out, and also minimizes the chance of bending any of the pins.
Now attach your heatsink/fan to the CPU. Use the method the other people suggested. You WILL have to apply some force most likely, (more or less depending on the type you have). These things need to be tight against the CPU core to efficiently remove the heat that's generated. But again, use common sense. We're talking about a fragile silicon chip here. If you're torquing that heatsink on there like you're trying to loosen a rusty lug nut, well, you're probably doing something wrong. Take your time. BE SURE TO ATTACH THE FAN TO THE CORRECT POWER CONNECTOR ON THE MOTHERBOARD. Some motherboards won't boot without the fan connected to the "heatsink/fan" header.
Now add your RAM to the DIMM slots. Check your motherboard manual first. Sometimes you must fill certain slots first... sometimes not. Always nice to know this before you go to boot and get a blank screen. The bottom of the RAM stick is keyed, meaning it can only fit into the slot one way. These usually take a good firm force to get them pushed all the way in. It's usually easiest to push one side in and then the other. Push straight down on the top of the RAM stick with your thumb, don't grip in on the sides (the whole static electricity thing again). You'll know it's mounted properly when the mounting clips are flush with the side of the RAM, locking it in place.
Now would be a good time to check your motherboard manual to make sure any jumpers that need to be set on motherboard are indeed set correctly. Check the jumper for the CPU multiplier, if you have one. It should be set to the correct amount, or set to BIOS if you plan to set it using the BIOS. Check the jumper for your bus speed/memory timing if you have one. Set it to the correct bus speed/memory timing (ie 100/100, 100/133, 133/133). Also set your onboard audio to enable/disable if you have it. Check everything, this is the easiest time to get at those jumpers.
If you have a motherboard tray, you can attach your video card and other PCI/ISA cards now, otherwise you'll have to wait until you get the motherboard back into the case. One thing to keep in mind is that some of your PCI slots will most likely be shared with other devices. For instance, slot 1 is usually shared with the AGP slot (video card). It's a good idea to keep that slot empty if this is the case. If you run into IRQ conflicts when you're installing windows later on, you may have to swap your PCI cards around.
BEFORE you put the motherboard into the case, mount all your other devices into the case. Get all those fans mounted, mount the floppy drive, hard drives, CD-ROM/DVD drives, ZIP drive, and whatever else you've got. Make sure you set your hard drive(s), CD-ROM/DVD drive(s), ZIP drive, etc for MASTER or SLAVE before you mount them. Figure out how you want them set up now. It's just about impossible to move those jumpers after the drive is mounted in the case.
Ok, now you've got all your harware mounted in the case, it's finally time to put the motherboard tray/sheet back into the case. If you weren't able to attach the video card and PCI/ISA cards before, do that now.
Now is when I hook up the case wiring to the motherboard. I'm talking about the power switch, power led, hard drive led, speaker, etc. Laying the case down on it's side will make this process much easier. This is probably the most confusing part of setting up your system for most people, but it really isn't. Look at your manual. Find the page with the diagram of what pin is what. Each of the wires attached to your case should correspond to a set of pins on the motherboard, and should be labelled. (ie, PSWITCH = power switch, HD = Hard Drive LED, etc) Abbreviations vary, but you should be able to figure it out. About now you're asking yourself, "Which way do I connect the wires? How do I know which color is positive(+) and which is negative(-/ground)." Easy. Look the black connector on the end of the wires. See the small arrow at the end of one of the wires? Connect this to the positive(+) pin on the motherboard for that set of wires. That's all you have to remember. No more guesswork.
Hook up your power supply to the motherboard. For an ATX power supply, the molex connector will only attach one way. Next attach all your drive cables and then your power cables (don't forget your case fans)
There you have it. Your computer should now be usable. One thing to remember. Don't go trying any overclocking until you're sure everything works. First priority is to get your system running stable... THEN overclock.
Hope this helps. Anything I didn't answer, feel free to ask. And sorry it got so long. (Hey, I was bored)