PS3Xploit brings homebrew to all models of the PS3 in the form of HEN, short for Homebrew Enabler! PS3HEN works on ANY model of PS3 as long as your console is on firmware 4.87 or lower. This tutorial will walk you through the process of installing 4.87 HFW, a hybrid firmware build of 4.87 which will allow you to install and run the required files. After being installed, this will cover the actual installation of PS3HEN, homebrew installation, and some quick tips on how to use PS3HEN! Although this tutorial was recorded with 4.86 all of the software needed has been updated to 4.87 meaning the steps will be the exact same. The only difference being a 4.87 HFW will need to be utilized as opposed to 4.86 HFW shown in this video.
Keep in mind this is not the equivalent of full custom firmware (CFW) or Jailbreak! PS3HEN does not have the full access CFW contains, but much of the functionality people are looking for is readily available in PS3HEN. Not all homebrew will work on PS3HEN, some of it will require either resigning to 3.55 or will need an update from the author.
As a final warning directly from the PS3Xploit team themselves: DO NOT UNDER ANY CIRCUMSTANCES ENABLE FSM (Factory Service Mode) OR INSTALL CCAPI ON A PS3 WITH PS3HEN!
PS3 models that can be jailbroken include the retro bowl following: Fat — All PlayStation 3 Fat models are supported. Slim — Your console is supported if the first two numbers following "CECH" are "20", "21", or "25", and if your PS3 Slim model is version 3.56 or lower.