1. Win games and your GM will gain a certain amount of points. 2. If you have a player win player of the week, your GM will get more points. 3. A trade where you win will get you 300 points. Not a lot, but it can definitely help. 4. An amazing game by players you draft will definitely get more points for your GM. 5. I can't confirm this, but I expect winning individual awards for players also will get your GM more points.
Gil Darnell is probably the best GM you can target after the first offseason. I'd get him first if you can. After him target Meese, Mikey Lewis, or the Texans GM(cant remember the name) in that order. Comparisons are key, so definitely get the Insider special skills.