Where have you been?? the moon or something.
I would consider soft modding a fat PS2 to be either using a swap magic disc to boot a backed-up game.
This involves removing the disc tray front dust guard (put it to one side incase if you ever want to re-fit it)
Then using a "slide tool" to open the disc tray without pressing the "eject" button. (the slide tool can be bought online with the swap-magic disks)
The websites that sell these have explanations of how to use the discs in this way.
Second Method,
Fit a standard PC Hardrive (Maxtor brand reccommended)to the spare bay behind the rear cover on a fat PS2.
you use a Sony PS2 network adapter as the method of connecting the HDD to the PS2.
Buy a software called HD Advance.
This will let you load games onto the HDD (back-ups or originals) and provide a splash screen interface to access, add , delete the games on your HDD.
The software will also format the PS2 HDD into the appropriate format.
HDadvance is just a knock off of HDloader. And besides you can download it for free and use it, as soon as you exploit your PS2. You could search for PS2 softmod on google. Or....just go to this tutorial click here. Its the easiest I found so far. All you need to buy is codebreaker. And a Hard drive if you want
That's a good guide link to follow.
I would recommend fitting a hard drive though because it saves your laser and most importantly, loading times are much faster and you dont need to worry about scratched , dirty , or damaged disks once the games are on the hard drive.
Whether you choose HD Loader or HD Advance to format the HDD and load / run games is up to you but you can't buy HD loader anymore, you have to download it, which means it is a back-up and needs a method of booting.
If you want you can still buy HD advance, and the fuss is over because it will be recognised by the PS2 as an original PS2 disk.