For the Karthan Ridge: Domination, you need to capture any of the five objectives and hold them for the longest time possible. In order to win, you need to reach 1000 points. Points are awarded for holding every objective for every tick. Killing enemy players will also give you on average around 2 points per kill.
Since there are 5 main points on this map, versus the Black Garden's version of Domination, what you will need to do is to move as one group to the center. When you jump down the ledge into the playing field, two people should split to grab the points on your sides.
After that, there is a second ledge that you have to jump to get into the center. By that time, you should be prepared to fight against the enemy to see who grabs the center point. The two people on the sides, if they can stealth, should then go and grab their outlining objectives. If they can't stealth but are DPS then when they enter the fight, that can be the additional push needed to win.
If you are on the Guardian side or Defiant, when reaching for your objective you will need to keep one person to grab the point as quickly as possible, and the rest of the sub-team to be prepared to intercept incoming players. Afterwards, always make sure you have one or two players holding or watching over the post.
Now if all goes well, you would have three main points and it would become a war of attrition...except that the enemy team, in order to win has to capture another point, so they will split up. When they split, that's when you should grab the outside points, force it to convert, and go back to defend your points.
3 healers, 1 support, 6 damage dealers. AOE attacks help stop the enemy from stealing the objective, but like The Black Garden, single target attacks are better for taking down targets one by one.