yeah you've got it pretty much right :)
when you take the top/side of the computer you should be able to identify the graphics card easily (it's the one the monitor plugs into!), it will be held in place by a single screw on the edge of the back plate so remove that, there may also be a plastic clip at the front end of the actual slot that you have to push to release the card, the card can then be pulled out, they can take quite a hard pull to get them to come out so don't be afraid to put a little bit of force into it!
once you have the old card out simply line the new card up with the slot and push it straight down until it is seated firmly in the slot, again don't be afraid to use a little force, they require quite a firm push to get them in.
once thats done turn on computer and install the drivers, either from the CD that will comes with the card or the ones you download if you get the latest