How to patch the game
Delta Patcher has been bundled along with the translation patches. The UI is relatively simple.
For the source file, select your CLEAN ISO. This means the ISO cannot be patched over a previous patch. It needs to be a newly ripped ISO. After you have selected the ISO you intend to modify, choose the patch you wish to use and press the "Apply patch" button.
If you wish to keep your original ISO after it has been patched, you can check the "Keep original file" box before you apply the translation.
How to run the game
The most popular method of running the game is via HDD on a fat PS2. HERE is a handy video that will teach you how to run backups off of a HDD. Playing off of a PS2 is recommended as it is the most stable method for running the game.
Refer to these links when considering what to buy: