Operation Flashpoint: Red River

The top rank for all classes is 20. Each class has B-Mods that increase experience. The first B-Mod gives you an additional 10% and the second, unlocked once you reach rank 13, nets you an extra 20%. I suggest equipping those as it will make you rank up faster.

By playing the campaign once you should have reached level 20 if you stuck to the same class. You get experience for pretty much everything, from killing to healing. objectives seem to give you the largest amount of experience so I suggest doing all optional objectives and healing your teammates yourself rather then ordering them to do it.

If you want to get this done quickly you can play Fireteam Engagement missions from the main menu. Combat sweeps are quite fast and easy. CSAR missions are also not that hard if you know what path to follow and have someone to blow up the chopper for extra experience. One Combat sweep or CSAR mission can be done in 8 to 10 minutes.

Many thanks to Defrosted Jay for pointing out that you can check your experience while in game. In order to do so, pause the game and pres . You will then see your Combat Experience tab. Here are the categories with experience gains I have observed so far;

Current Kills XP
How much XP you get depends on the type of kill. You can get a normal kill, headshot kill, vehicle kill, and explosive kill.

Current Objectives XP
Main objectives and optional objectives give you experience points. How much will, at least for FTE missions, only show as a sum at the end of the mission. During campaign you will receive stepwise XP every time you complete a major objective.

Current Teamwork XP
- Stopped bleeding on teammate 22XP
- Heal teammate (orange) 22XP
- Heal teammate (yellow) 22XP

Current XP Penalties
- Squad death (varying) Note: Reviving a team member while he dies nullifies the penalty.
- Friendly Fire (-50XP)

Survival Bonus
As suggested by tweekfu, you receive a 10% bonus up to 30% for each mission you survived beforehand.

Actions with no observable XP
- Healing self
- Ordering teammate to stop your bleeding
- Repairing vehicle, self and teammates
- Orders of any kind

Review 25 September 2014: Added button icons.