First things first, let’s check if you have everything in order to jailbreak your ps3.
Do you have the original 3.55 firmware?
(if your not sure, go to system settings on your ps3, then scroll down to system information and it will display your firmware version)
If true: go to part B
If not true: have you updated PAST 3.55? This jailbreak method is not for you
If not true: do you have a version BELOW 3.55? Go to part A.


Part A, updating to 3.55

Yes?!, you have a version below 3.55? Then we should update to 3.55:
*
Make sure your USB has the format Fat32
Download the Official firmware update version 3.55 or from this link: OFW 3.55
Put the update file named “PS3UPDAT.PUP” on your USB in the map PS3, and then the map UPDATE
So the path would be ”X:/PS3/UPDATE” (X representing the letter of your USB).
Connect the USB device to your PS3 and update your ps3 using the option “Mass Storage Device” (Go to Settings->System update.
Follow the prompts.
When done, you should have version 3.55. Awsome! Let's continue!


Part B, getting the CFW 3.55 ready for jailbreaking your ps3

When you have version 3.55 installed: we will use Prepatched k-3.55 Custom Firmware (CFW) (from K-meaw) to jailbreak your Ps3
Download here: Kmeaw Custom Firmware (CFW) 3.55* * *
Connect your USB to your computer and make sure your USB has the format FAT32
Put the update file from K-meaw named “PS3UPDAT.PUP” on your USB in the map PS3, and then the map UPDATE
So the path would be ”X:/PS3/UPDATE” (X representing the letter of your USB)
Connect your USB to your Ps3 and go to the Ps3 Recovery Screen

Part C, getting into the Ps3 Recovery Mode screen and installing the CFW
To install the CFW you have to boot your ps3 into the recovery mode.
Now go to your Ps3 console and turn it off.
Next, hold down your power button until your Ps3 turns on and then beeps 3-times and turns off again.
Let go of the button when off.
Now hold down the power button until the Ps3 beeps once and then twice and then let go of the button.


You should now see the recovery screen.
If it asks you to plug in your Controller remote, then do it and hit the PS button.
Scroll down to option (6) System Update and hit X.
Follow the prompts.
Once the update is finished, your Ps3 will reboot.

You just did the ps3 jailbreak method! Excellent.

Easy way to Verify that you have the Jailbreak... Look for these two items under your GAME icon
1) Install Package Files
2) /app.home/PS3_GAME/

Any .pkg file you want to install, just put it on your usb drive and go to the " Install Package Files " button under games on your xmb.

EDIT:
When using this method you have only made your Ps3 ready for homebrew games etc...
But to play backup games etc... you still need to install a proper BACK UP MANAGER -->> HOW TO INSTALL MULTIMAN .... backup manager for Kmeaw's CFW 3.55 - PS3 Jailbreak Community