Shift to the smallest cog. It shouldn't matter which chain ring you're on since the right shifter controls the rear derailleur.
Loosen the binder bolt on the rear derailleur to free the cable. If there's one of those caps on the cable remove it as well.
Pull the cable out of the cable housing located on the rear chain stay.
Pull the cable through the guide located on the bottom of the bottom bracket shell (if there is one one the bike).
Depress the brake lever as far as you can (You might want to remove the rear wheel so you'll have more travel in the lever)
Push the cable towards the front of the bike. Do this right where the cable comes out of the housing on the down tube.
Remove cable and replace with new one. Note: finding the hole when reinserting the new cable can be a little tricky (at least to me it was). Once you remove the cable shine a flashlight into the front of the shifter to see where the new cable needs to go.
You shouldn't have to replace the housing.
That should give you a good idea how it's done. I'm sure if I left out anything really important the professional wrenches here will let us know
Zack