I was wondering how the locker system works in BSB.
Do we get assigned lockers, or is it a first come first serve basis to whoever gets to the lockers and places their locks on them?

You definitely can't just claim an empty locker and put your own lock on it. All the the locker allocations are done through Titles for almost everywhere on campus, and you have to rent them for the year - see here: http://titles.mcmaster.ca/geninfo/lockers.htm