1) turn off computer
2) unplug computer
3) Open computer
4) Place computer on flat surface (not carpet!!! A table or a wooden floor should be ok)
5) ground your self and put on gounding wristband thing if you have one
6) try and handle the ram in the antistatic bag it came in
7) undo the clip things on the mobo in the ram slot (and take out old ram if applicable)
8)push new ram in making sure that the pins are alligend with the slot until it kinda clips into place
9) close computer and turn it back on
10) verify that you have added ram in the bios ( it will say for example "new ram detected 1024mb detected press ok to continue" or something like that)
11) continue use of your pc (if your pc spontaniously restarts or you get blue screens of death then your ram could be corrupt)

Except for this one very important step:

If you have a large(ish) add-in display card be very careful not to damage either the display card or the RAM slot clips when installing new RAM modules. It is better to remove the display card, fit the RAM module, then replace the display card. That way nothing gets broken