This is a little compilation of what will help your rank and what will hurt it. Hopefully this gives you a little insight about the new system.
Help your rating

Play in full rooms. This means play in 11 round, 6 minute games as per default settings.

Always be stealthful. Although you can play anyway you choose, this style helps maintain kills over deaths.

Learn to snipe properly. Distance kills with a rifle helps you out a lot. Especially larger maps like crucible, killing fields, devils road.

Try and get behind your enemies. During the game try to take shortcuts or back paths to get ahead of or behind your enemies.

Know your maps. If you know the maps well you can use it to your advantage. Position yourself into a strategic position and wait for convoy trucks, bomb plants, ect.

Aspire for MVP. Although you may not achieve it, wanting it helps you do better during games. Motivation is a must.

Don't get aggrivated with the game. We all get pissed off sometimes, but try and control it. No one can play better when they are aggrivated, so keep your cool.

Don't try to be a hero. Rushing out and getting yourself killed is not the answer. Socom3 is a game based on teamwork, remember that.

Know your place. If there is 1 minute left on convoy, don't run out to kill the terrorists. If there is 30 seconds left on demolition and you are outnumbered but have the bomb, stay hidden. Knowledge is everything.

A tie is better than a loss. Like above, know your place. Don't try and win if the odds are against you. Let the game play itself out.
Hurt your rating

Playing rank up games hurts your rating badly. You can tell who ranked up to an officer position if they have a rating below 500. Always play legit, or you will be moaning later because you will never leave ensign. 3 round 3 minute games demolishes your score.

Rushing out and dieing or trying to be the hero will eventually hurt you. Kills over deaths is almost a necessary thing to getting your score up. Don't voluntarily ruin it.

Being the idiot on the team. If you are the person that steals the vehicle and crashes it into the water or uses it to drive 20 feet, just stop it. You need to work and strategize with your team. Don't deprive them of a vehicle just because you don't like to walk. This will lead to a loss nearly everytime.