You need a ps3 with firmware 3.55 or below if higher you need to see if your ps3 can accept firmware 3.55 or below. If it came with a firmware higher then 3.55 then you can not jailbreak at all. If 3.55 orlower was on it at one point you need to buy a downgrade tool and solder it in or have someone do it for you. There are no software methods above 3.55 nor will there ever be one due to the security is now properly implemented unlike 3.55 and below. The only other option is to buy and solder in a ODE like Cobra ODE. And you can play online with a hacked system but you can be banned in a heartbeat especially playing Call of Duty. That is almost a instant ban for that game.
PS3 CECH-2501A [CFW] & CECH-3001 [OFW]/ PS2 SCPH-3901 & SCPH-7501/ PS1 SCPH-5501
Mod Cobra 4.46 v7.00 w/ E3 Flasher [CFW] & Cobra ODE 4.50 [OFW]/ Mod HDD-OSD [Phat] & Modbo 4.0 [Slim]/ Mod MM3
HDD 1tb [CFW] & 640gb [OFW]/ HDD 640gb & OPL v0.92 w/ 1.5tb SMB