Without going down the rules bit in a long fashion, the core of the game are the missions you run with your leaders. The leaders are either Admirals or Generals. A leader during the mission phase has two states: assigned to a mission, and in the pool. Leaders in the pool can either move fleets or oppose enemy missions.
The 2 player games works like this:Rebels use a leader. Empire uses a leader. Rinse and repeat.
The 3-4 player game order works like this: Rebel Admiral Leader phase, Imp Admiral, Imp General, Rebel General. I may be off on the order, but the premise is the same.
There are some actions in the refresh phase assigned to the Admiral and General players, but it's not important.
It's actually not all that bad, and 90% of the time it works ok. Where you get boned is if there's a set of missions you want to run a particular order, you have to pay attention to how you queue them up. Each leader has stats that affect the mission outcome. In a 2 player game, I can line up the missions based on stat, in a 3-4 player game I need the line the missions up based on if I want the first mission to be done in the Admiral phase, then the stat, and then the general phase. What I do like is you kind of get two separate actions per turn. That one/two punch can be handy.
I don't mind the game 3-4 players. Especially on the imp side it's handy to have someone keep track of the probe cards (the cards you use to eliminate where the rebel base is), or at least help with bouncing ideas off of "I think the rebel base is here).
That said, in a convention environment my main goal is to teach people how to play the game so they can decide if they want to play it. The games are clearly marked "teaching". In this case, I''ll take a game that shoehorns a 3-4 player game over just letting one player play it.