A PUG is a (P)ick(U)p (G)ame. See this thread for more information about the origin of the term:
https://forums.sinsofasolarempire.com/354207
Basically, it's a way of trying to end disputes about who should be on which team while also balancing the distribution of talent and skill between the two teams with the goal of having a better game. The way we do it is that everyone starts off on Team 10 and two people become team captains and choose a team number. A non-captain chooses a number from 1-10 and /w whispers it to another player. The two captains then pick numbers (normally 5 and 6) and whichever one is closes to the chosen number decides whether to pick first or defer to be the second captain.
For a 5v5 the draft order goes like this: A-BB-AA-BB-A with the first captain (A) having the first pick, with the second captain having the next two picks (2nd and 3rd picks), and so on with the first captain getting th last pick (sometimes affectionately referred to as "Fat Boy", just like in gym class).
Most 4v4's use a slightly different draft order: A-BB-A-B-A.