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.