Aarhus

Maybe I can give you confidence. Batteries, RAM upgrades, and heatsink swaps are great starting points for anyone.

1. Remove the back panel - if the screws come out of the cover, put them in a cup or on a piece of tape and watch for longer screws and remember where they go. If they don't come out, still try not to turn that piece over as captive screws aren't always held in well
2. Ground yourself by touching a hinge, or attaching your ESD wrist-band there - only to the metal
3. Disconnect the battery
4. Trace old fan cable and unplug it from the main board
5. Unscrew the 3 or 4 larger screws with tension springs around the outside of the heatsink and remove it (a little slowly, some thermal paste dries more and makes this difficult)
6. Wipe off old thermal paste with alcohol wipes and let dry
7. Peel plastic off new thermal pads and place them (or apply a thin spiral of paste) on each silver cap of your CPU
8. Center the new fan over the CPU and check your wire isn't underneath or in the way of a screw
9. Screw the heatsink down and reconnect your fan
10. Reconnect the battery
11. Test
12. Put cover back on

The main things are grounding yourself, not touching anything you aren't working on, the battery (disconnect first, reconnect last), the plastic wrapping on thermal pads, the fan wire (just pay attention to it), and testing first. The computer will check the fan as soon as it starts, and they are usually set to shut down if overheating.

You'll spend less time than I took writing this, probably. Good luck