While the PCSX2 code is completely legal, Sony owns the code of the PS2 BIOS. It also touches on the one complicated part of setting up the emulator: the PS2 BIOS. Here’s a great guide that lays out the basics of configuring PCSX2 and its graphics settings without overloading you with information. Mostly all you need to know to get started is how to configure the graphics settings and a gamepad.
The official PCSX2 guide is a great resource, but filled with an intimidating amount of information you don’t really need to know if you’re just out to play games.
Download PCSX2 here and follow a configuration guide to set it up. The rest of the process is pretty simple, honest (at least, unless something goes wrong).