What is the basic idea of playing Dominion? What I mean is just like Summoner's Rift has it's meta and lanes, does Dominion have something similar? All I know is that generally 1 person goes to the bottom but what does everyone else do?
From my experience in dominion (just like in Summoner's Rift like you mentioned) there are some basic champion Roles.
In Summoner's Rift you have your:
You also want to have a good amount of CC and aoe because there are many teamfights and you will need a good bruiser and a tank (usually being the solo top - jungler) That's just roughly ofc.
In dominion you have the following roles:
A capturer is a mobile and sneaky champion with good escapes who can roam the map and capture unprotected capture points. Good picks would be Teemo, Janna, Evelyn, Rammus etc
A defender is a guy who can fortify himself under a capture point and defend it for a long time against 2 and maybe 3 opponents. Good picks would be heimerdinger, Alistar etc.
Taker is champion who can effectively dive a capture point and take it even when a defender is under it. Good picks would be Darius, Xin Zhao, Tryndamere etc (You get the point)
The ideal analogy in a team (in my opinion) would be 1 Capturer, 2 Takers, 2 Defenders. If your defenders are good then they can pretty much camp and lock 2 out of 5 capture points. This might sound trivial because the other team would still have 3 and be winning. But if you can lock 2 capture points for a long time using just 2 champions, then you give your 2 Takers the luxury of invading the weakly defended capture points of the opponents together. 2 GOOD takers should be able to take a third Capture point at all times.
If the opponents group up to take one of your Defenders down they just make your Capturer's job easier since he will most likely find at least one capture point unprotected.
Also much like in Summoners Rift you want champions with Aoe and CC, in this map you want mobile champions and champions who excel in small fights 1v1, 1v2 etc. AOE is not needed much in this map.
Also champions with universal spells (ults) can come in handy if they can effectively fill some of the above roles...
EDIT: You seem to wonder about possible opening strategies in dominion. Well the standard way to open up is that a good defender goes and captures bot and tries to push the lane right after that. Thats why heimer is such a good pick for this role.
3 rush top to cap as much of the capture point as they can and fight and 1 caps mid in a hurry and then joins the other top.
Some teams however prefer other strategies. One of would be only 2 to rush top, 1 bot, 1 mid and your capturer would go in the jungle and wait for THEIR mid to finish capturing. When they mid goes top to help the others your capturer goes in and caps their unprotected mid. At this point at least one of them would probably turn back to stop him so the Goal of your guys at top (including the one coming from your mid) is to prevent any fleeing champs from getting there fast. Its not your goal to capture top but to delay them.