Put basic stats like win difference, games played, Dom rating if available, preferred roles and your best champions on your open resume. It also helps to include your times of availability for team practices and forms of communication you're willing to use (vent, skype, etc.).
It can be difficult to get a foot into an existing tournament team because most regular teams have their core lineup already and if they need subs they already have a network of people to ask. There's a fair amount of teamless people though, so you might consider throwing together a team of randoms from DD chat or solo queue and trying a few tournies. The more experience you and your team has with tournaments, the easier it will be to recruit and improve.
LoLRecorder is pretty common. I haven't used it in a long time but my teammate MMKH usually records every game we play as a team. I know Feedski occasionally asks him for replays of tourney matches.