Thuc: you play 4 games against the same 7 people in a league. You are then scored as per in the website, and depending on how you do, stay in the same league level, get promoted or get relegated.
There are currently 5 league levels, Premier, A, B,C and D. A fifth, E, might be added.
B, C, D and E are split into more than one league, so that people can rise to the top more quickly after joining. Hence C1, C2 and C3 etc. they are the different C-level leagues.
I've got to sleep now, I'm sure current players will help by answering questions. :)