This is intended for those who wants to update to firmware v3.41 in order to use the PS Jailbreak exploit (such as PSGroove and PSFreedom). Note that this has nothing to do about updating to v3.42 or later versions, there is no way of doing that safely yet.

1. Download firmware (PS3OS) v3.41 from Sony
2. Check that they haven't patched anything by verifying the MD5 checksum of PS3UPDAT.PUP which should be e07d2b84c9e9691c261b73e5f1aada20. Eg. use 'md5sum' in linux. On Windows start a Command Prompt and use file found here, like this: md5sums PS3UPDAT.PUP
3. Copy the file PS3UPDAT.PUP to a USB hard drive or flash stick, the file system should be FAT, and the file has to be located in this directory: \PS3\UPDATE\
4. On the PS3, insert the hard drive or flash stick in a free USB port and choose; Settings->System Update->Update via Storage Media, and start the install.


If you skip step 2 there's no point in doing any of this. If Sony (which is likely) have patched the update to block the PSJailbreak (or PSGroove) exploit without updating the version number you will probably have to buy a new PS3 if you want to use this hack.
Mini FAQ

Q: Why not just use a file sharing service like rapidshare or similar and post the file there?
A: Because the link will be dead in no time considering the traffic (or because of Sony). Probably a lot faster to download from Sony as well, just check the file MD5 as instructed.