Any time you're going to be working with sensitive materials, make sure to take precautions against ESD. Work on a surface that isn't going to build up a big static charge, don't wear a big fuzzy wool sweater, etc. Before you touch any components inside the case, touch a piece of unpainted metal on the case first. I imagine you did all of that before working with your RAM and graphics card, so you should be all set there.
Here's a video created by Intel showing how to install and remove an LGA775 processor:
http://www.youtube.com/watch?v=OFEOd7nQbuQ
As far as the motherboard, it's pretty straightforward. Disconnect everything, remove PCI/PCI-e cards, unscrew every screw holding the motherboard down, and then carefully lift it out of the case.
At this point I would inspect the motherboard tray inside the case for two things: first, make sure there's no foreign matter, like a screw that may have fallen behind the board. Second, make sure that the standoffs line up with the new board. If they don't, move them around so they match the screw holes in the new board. Standoffs which are not lined up with your motherboard's mounting holes stand a good chance of shorting it out.
Now pop out the old I/O plate from the back of the case and pop in the new one. If they're stubborn, a couple love taps from the butt of a screwdriver sometimes helps.
A lot of people like to mount the drives in the bays before they get the motherboard, CPU, etc. in. It's a matter of personal preference, but it may be a little bit easier to do it first.
Before you actually install your new motherboard into the case, most people like to mount the CPU, heatsink and RAM on it. It's much easier to do outside the case than inside it. Once those are securely in place, lower the motherboard into the case onto the standoffs. Screw the motherboard into the case, making sure that it fits into the I/O panel correctly, but don't fully tighten it down just yet. Connect your video card and line it up to the slot in the back of the case, and then tighten the motherboard down. It's not strictly necessary to do things that way, but it can help avoid having your video card be slightly out of alignment with the expansion slot.
Carefully connect all the power cables, including the 24-pin ATX connector, the 4-pin +12V connector, and the 8-pin EPS connector if you need it. Then connect all the leads from the front panel to the correct pins on your motherboard. They should be labeled on the board. Polarity (+ vs. -) only matters for the LEDs, not the switches. As a general rule, white/black wires are ground while colored wires are positive. This isn't a strict requirement though, so consult your case manual if your friend has it just to double-check.
Now just connect up your drives and you should be good to go. Don't forget to make sure that the PSU is on once you attempt to boot the computer.
Some people like to test the motherboard, CPU and RAM together outside the case before installing everything. It's called bench-testing, and it's not a bad idea. You need all the power connectors plugged in, along with the CPU, heatsink and RAM, and the power switch lead. If you want video output to confirm that things are going smoothly, you'll need your video card of course. If everything works outside the case but doesn't work inside of it, make sure that there's nothing that could be shorting out the motherboard.
I'm not fully awake yet, so if I left out a detail or two someone will be along to help me out in a minute.
