To level up quicker than usual, try to use the same gun until all the marksman and elite challenges are completed. They provide huge boosts and will quickly level you up to get new guns. However, do not use those guns yet. Just keep on the challenge until it has completed. The third phase of the challenge usually ends with 1,000 experience points and that will bump you up a rank almost in itself. Also, do not forget about the strange challenges like jumping 15 feet and surviving or falling 30 feet to your death. To get that one if not previously unlocked play the "Countdown" map and jump into one of the open missile silos. You will get instant experience points for simply dying. Also, remember to go prone and crouch to get those challenges as well.
To level up, gain points, and to complete challenges easily, find a TDM game of the map "Shipment", preferably with a lot of people. Make sure you have the Steady Aim/Martyrdom/Stopping Power perks on and choose a gun you want to level up. Shipment is a very small close shoulder-to-shoulder map. Just run around holding down the trigger, taking down as many people as possible. This is very fast paced and you should tick points very quickly.
Playing games such as Sabotage and Ground War will give you lots of experience points because both games offer many kills. Sabotage has a long clock, giving you the opportunity to get many kills or challenges. Also, look for Sabotage on the Wetworks map. That map takes a lot of time up.
Use the following trick to level up and increase your Kill-Death ratio. Cook and hold a grenade at camping teammates, then throw it at them. Quickly switch teams and the grenade will become an enemy grenade and kill them. You will not lose points for switching teams and can rack up huge kill streaks. You can also get all of the bonuses such as Airstrikes, UAV, and helicopter. Note: This also works when using an airstrike. Call the airstrike on your team, then switch teams to kill them.
Play Headquarters when it becomes unlocked. In this game mode, for every five seconds your team holds the headquarters you will get +5 experience points. If you are on the winning team (a team wins when they reach 250 points), you will get 250 experience points plus whatever amount of kills you get. If you are unskilled and cannot manage to get kills, you will still get points simply for being on the team that holds the headquarters. This is a gamble though, because your team may go the entire match without ever having held the headquarters, resulting in no experience.