I followed this guide when I softmodded my PS2 a few weeks ago.
https://www.youtube.com/watch?v=QPPfmKmiQY8
It went through perfectly the first time. In order to use Ulaunch to install Free McBoot, you need a flashdrive with Ulaunch and McBoot on it, a PS1 game (could be any PS1 game but it has to be retail. Burnt games or ISO's won't work), an empty Memory Card and you need an Action Replay Max or Evo disc for PS2, that has the USB option and can read your USB drive. This video should help you set this up. One CRUCIAL thing you need to know about setting up MCboot. Your formatted Memory Card has to say "MagicGate" on it. Reason why is because Free McBoot only reads and edits MagicGate Software. If your MC doesn't have MagicGate labeled on it, it's most likely a fake or Chinese Import. I made that mistake when I bought my second MC on Amazon. If you try to copy the files on that kind of MC, the system won't boot the software and will put you on a blank screen. You'll probably think that you bricked your PS2. In that case, just remove the MC, and reboot your system and it should be fine.
-Speaking from Experience.