Crash course: Right-click capture points to start capturing. There will be a short channel time before capture. Champion damage can interrupt it.
Dominion has increased health and magic regen, Lifesteal, spellvamp, and heals are nerfed. There are various consumable health sigils on the ground, and speed boost pads in strategic locations.
General consensus is 4 top 1 bot.
Bot lane should be able to defend their tower with sustained damage and have decent sustain/sniping capability. Heimer is infamous for having impossible-to-cap points, especially when he gets two turrets. Morgana and Caitlyn are also picks I've seen work really well, along with most tanky DPS. I've gone bot as Mundo and did fairly well.
The person who has the least to contribute to the teamfight will cap "mid" on your side. Just make sure you know who's capping it before the gate goes down.
At top: First priority is getting the tank in, start capping that point. If you're obviously behind for some reason (teammate left behind, someone died early) you may want to just retreat and regroup. Push again later.
"Backdooring." This has been made less of an issue with the cap speed boost item removed, but hard-to-catch champions like Shaco or Rammus can still pull it off. If your team is preoccupied top and the enemy team isn't paying attention, cap another area. They should be able to defend with 3 + turret, at least until you're done capping and can help.
My favourite champion on Dominion is AP Kog'Maw. Nashor's -> Zerks -> Tear -> Chalice -> Morello's. You see what I'm going at here? With the increased mana regen along with a ton of mana regen/CDR items you have the longest range spammable spell in the game. Who needs damage when you can rain death on them from afar?
Close second is Rammus, though he's used a lot and is almost ALWAYS picked during freeweek due to his speed.