There's an old saying that goes "You can't take it with you when you die," but we disagree. Sure, you might suffer an XP loss or have a nifty +3 bastard sword disappear from your inventory, but all in all, your belongings remain intact in the event of an untimely character death. The saying should be "You can't take it with you if you don't save your game data." We can't help with your lack of FPS skills, but we can help you transfer your game data to a new PC or hard drive.
Find Your Save
Backing up a save game is easy; finding the location of your save data is the tricky part. Game makers just can seem to settle on a common saved game spot. A tremendously handy tool called GameSave Manager can autodetect and back up most of your saves into an easily transferrable archive, but it has been known to miss some more obscure games. If you need to manually track down a sneaky save, there are some common locations for saved games in Windows 7 and Vista, such as:
Your save games usually hide deep in the recesses of your Windows User folder.
C:\Users\%User Name%\Documents\My Games\%Game%
C:\Users\%User Name%\Appdata\(either Local or Roaming folder)\%Game%\
Sometimes, game developers like to get tricky by hiding a game's folder inside a folder named after the publisher, changing the filepath from,say, Appdata\Assassin's Creed to Appdata\Ubisoft\Assassin's Creed – consider yourself forewarned. Also, games that save to Steam's cloud service, such as Left 4 Dead, save to numbered folders in the C:\ProgramFiles\Steam\userdata\%SteamUserIDNumber%\ folder.
Once you're inside the folder for your game, looked for a folder entitled "Save Games," "Userdata" or something along those lines. Backup the save files using the standard methods; flash drives, CDs, FileHost, whatever.
If you can't find your saves anywhere, hop online and check out a forum for the game you want to back up – you're bound to find a well-intentioned regular who can help you lay your grubby fingers on your precious save data. Or, you could just check out the massive list of save game locations painstakingly put together by Steam forum-goer Kailieann if you're the less social type.
Moving Steam Games
Transferring up your Steam games themselves is almost as important as transferring your save data. Sure, you could log into Steam on your new computer and redownload your entire collection, but that involves a ton of wasted time and bandwidth. Fortunately, moving your Steam games to another hard drive is straightforward.
A Steam folder that isn't quite ready for transfer.
Basically, you want to transfer your entire steamapps folder to the new PC. Before you try it, go ahead and back up the contents in the folder. Valve recommends it and so do we. Next, exit Steam and delete everything in the main Steam folder except for Steam.exe and the steamapps folder. Afterward, transfer the entire Steam folder to your new PC using your method of choice (though if you've got scads of 10GB+ games, an external hard drive may be your best option). All you have to do now is sign in to Steam on your new PC; after some quick updates, you'll be back to fragging box-hopping creeps in BRINK in no time.
That's better -- this Steam folder's ready to move.
Take note: this transfers your game data, but not your save games themselves. You'll still need to move those over separately.
Keep Your CD Keys In Order
If you've lost the CD keys that came with your non-Steam games, you'll want to download GameKeyRevealer before switching hard drives. The app extracts your installed games' CD keys from the Windows registry. GameKeyRevealer's a bit slow to add updates for new games, but its list of supported games is second to none – it can find the CD keys for over 1000 games.
GameKeyRevealer in action. Image Credit: GameKeyRevealer
Using it is simple; download GameKeyRevealer from its website, then unzip the archive. Boot up the GameKeyRevealer and click the "Find Games" button. Boom! Done. GameKeyRevealer will display the CD keys of any supported games it finds on your computer. Jot those keys down and be more careful with them this time!
And that should do it. Go forth and conquer with the knowledge that your game data is safe!