Taking things out of a PC's system block is nothing difficult. Correctly putting it in can have come intricacies, with choosing what to buy as a replacement is being the hard part. I'm not really knowledgeable enough on the subject to give advice an anything but the first part though.
Basically, you just turn the thing off, pull the main power plug out, disconnect all the cables from the tower itself and move it to the table you'll be working on. You might want to ensure that the place is well-lit, dry, without too much dust and litter around and you are not disturbed by any obnoxiously playful pets or people while you work. You will need a screwdriver (you may want to double-check if it actually matches the screws you'll be working with before you start) and something you'll put all the screws you'll be removing in so they won't roll away somewhere the moment you turn away from them (an empty matchbox usually would do fine).
After that you'll just have to methodically unscrew all the screws that will prevent you from pulling the thing you want out (for a graphic card about 5 - two or three for the side lid to access the guts and one or two that could be providing additional grip for the card to hold onto close to the side all the ports are sticking out of - or so screws is likely). Maybe you will have to unplug a power cord or two leading to it from the power supply.
About the only thing you have to worry about in this process is the strength of your fingers - newer produced modules generally tend to have less and less empty space on them to comfortably grip them with each passing year for some reason. So if you happen to run into a particularly stuck plug or socket, you may have to ask for help someone with stronger hands.
Either way, you shouldn't pull any plug just by its cord and you should slowly rock along the longest side anything that's not strictly circular or square when you pull it out.
EDIT:
There may be stickers saying something like 'warranty would be void if you break this';
in some cases they are stuck on the outer lid, preventing you from opening the guts up, especially if the PC was bought 'as is' instead of each component bought and installed individually. Unless the thing went dead on you before its warranty ran out, you don't need to worry about any of that.
Basically, you just turn the thing off, pull the main power plug out, disconnect all the cables from the tower itself and move it to the table you'll be working on. You might want to ensure that the place is well-lit, dry, without too much dust and litter around and you are not disturbed by any obnoxiously playful pets or people while you work. You will need a screwdriver (you may want to double-check if it actually matches the screws you'll be working with before you start) and something you'll put all the screws you'll be removing in so they won't roll away somewhere the moment you turn away from them (an empty matchbox usually would do fine).
After that you'll just have to methodically unscrew all the screws that will prevent you from pulling the thing you want out (for a graphic card about 5 - two or three for the side lid to access the guts and one or two that could be providing additional grip for the card to hold onto close to the side all the ports are sticking out of - or so screws is likely). Maybe you will have to unplug a power cord or two leading to it from the power supply.
About the only thing you have to worry about in this process is the strength of your fingers - newer produced modules generally tend to have less and less empty space on them to comfortably grip them with each passing year for some reason. So if you happen to run into a particularly stuck plug or socket, you may have to ask for help someone with stronger hands.
Either way, you shouldn't pull any plug just by its cord and you should slowly rock along the longest side anything that's not strictly circular or square when you pull it out.
EDIT:
There may be stickers saying something like 'warranty would be void if you break this';
in some cases they are stuck on the outer lid, preventing you from opening the guts up, especially if the PC was bought 'as is' instead of each component bought and installed individually. Unless the thing went dead on you before its warranty ran out, you don't need to worry about any of that.
