What if the Samsung Galaxy S I've got has already been rooted?..
Is there perhaps a special boot mode which would boot into the system with root access?
Or normally, a "rooted" device always boots the system with complete root access?
There isn't a special boot for rooted devices AFAIK. Any rooted device necessarily boots with complete root access.
If you want root access on a production phone, then you are going to have to use a root kit. There are a ton of benefits to having a rooted device, but there are also risks. Some devices are now coming out with the ability to run an app in root mode with user permission.
MY WORD OF CAUTION:
Attempting to root your device without proper knowledge will render it completely useless except for holding down your papers on a windy day. Make sure to do all instructions exactly and only flash your phone with builds that are meant to go with your specific device!
Best of luck!