There are many ways to earn extra XP and help you get through a prestige in a timely manner. Just as long as you are a decently competent player, these tips will help you rank up.
1) Gametype Playlists
It seems almost obvious to find what your best gametype is and play that over and over again. However there is one gametype that is simple and always dishes out good XP, Kill Confirmed. "Team Deathmatch with a twist". Kill Confirmed gives you 50 points for every kill, 50 points for confirming or having a kill confirmed, 50 for denying a kill, and if you manage to pick up your own tag you get 250 points. It also last a rather long time so plenty of time in game.
Modern Warfare 3 has so many challenges within it. So definately look into switching up your arsenal to complete challenges, especially weapons. This means using weapons and equipment that may or may not be stellar. While this may upset some, i only have to argue that nobody cares about their KDR, and should use some lower tier things. Every weapon has challenges for using the gun and with all the different attachments. A handy way of killing two birds with one stone is using the attachments proficiency to complete two attachments.
In MW3 there are 3 different sets of bonuses for earning points. These are the Assault, Support and Specialist packages. I cannot stress enough that unless you average a KDR ( and I know I said they dont matter) of at least 1, DO NOT use Assault. You will not earn Pointstreaks and subsequently not earn points. Support allows you to get your streaks just as long as you earn enough points in the game. There are very good streaks within Support as well. My personal favorite setup is the Ballistic Vests, SAM Turret, and Recon Drone. Ballistic Vests add 50 points of resistance to your team and you get 50 points for every vest taken. The SAM Turret protects you from annoying enemy UAV and air support, plus giving you points for destroying them. Finally the Recon Drone allows you to pilot a mini RC helicopter and "tag" enemies. The enemies are flashed momentarily, marked for your team, and you get assists for when they are killed. A viable option is the Escort Airdrop, which is when an Osprey delivers 4 care packages and a hacked package. Take the really good stuff, and let your team take whatever is left for Share Package bonuses and well as you get a kill from the hacked package and also the protective Osprey Gunner. A plethora of points! My arguement for specialist is, they are fairly low streaks, and when you earn perks, you can complete challenges for the perks. While also the all perks bonus gives you double XP for everything.
4) Mountain Dew!
Not only a very tasty beverage but you get double XP for each bottle! Double win in my eyes.
Using these tips I was able to prestige in about 5 days, 1 and a half in game days.