Open the program, hit "jailbreak" and follow the onscreen instructions. And no, you do not need to install Redsn0w, it is a standalone executable file, you just download and open it.
Download from here [Moderator edit: Removed link to external tutorial. We have our own here! Thanks.]
run it, click on "jailbreak and install cydia"
When it asks you, in the window that pops up on the computer during the process ONLY TICK "Install Cydia" and proceed.
Once it is done and your phone is in the lockscreen you are done.