Any way you need a jailbroken PS3 already so you can run multiman, black box FTP, GAIA, or any other backup manager because I'm certain they all include FTP servers.
FTP stands for file transfer protocol and you use an client on your PC to connect to the PS3 FTP server. I use filezilla but a google search for free FTP client will locate a dozen or so you don't need anything advance. Windows XP and I assume Vista and 7 have an FTP client built in. Just type FTP://192.168.0.55
in the address bar or internet explorer or my computer. Change the 192.168.0.55 to the IP of your PS3. The built in client kinda suxs and freezes sometimes but it is easy to use.
After that you'll see a few directories listed as flash 1, 2, and 3. Just copy those to your computer and save them. You can copy the whole hardrrive too which is a good idea but not really needed. Your choice.
After that you can upgrade and downgrade all you want (not 3.56!!!) and just copy the flash 3 back to the PS3 to restore DVD and Bluray playback.
Beware that downgrading on a slim erases your harddrive. So back it up first or start fresh. If you back up with FTP you can change your user name, PSN name, and still keep your trophies but save games won't work. There is work arounds but those answers are all in the forums.
Saving the flash and Harddrive won't restore a brick so don't get brave and do something stoopid :P If you try to downgrade to an earlier firmware than it came from factory the slim won't take it. Just try another firmware with the downgrade instructions.
Mine cam factory @ 3.40 I tried 3.15 and it failed. I just put 3.40 on the stick and tried again and the PS3 came back to life and worked.
But don't mess with 3.56 there is no downgrade for that yet and your PS3 will be stuck.