Its very possible to go prestige in a little over a day. My girlfriend got pissed off at me one day and left (don't worry she came back =D ), I ended up going from level 1 - 64 in a single day (lots of redbull and jerky).
As far as how to do it, thats best determined by your skill level. I sit around a ~5 (xbox 360) k/d ratio, meaning the way I level up fastest is to play regular team death match and use as many of the best guns in the game as you can. Don't forget that if you suck with a gun, grenade launchers still count as kills. In addition every 500 kills gives you +10,000 experience, and 500 kills themselves are worth 50,000 experience (100,000 on double point weekend). If you are a fairly good player (and playing with fairly bad players) you can exploit how over powered the kill streaks are in this game.
I tend to use UAV, Predator, Harrier; (against good players or bad players who shoot down every bit of air support)
Predator, Harrier, Pavelow; (in levels with lots of buildings where choppers suck)
or Predator, Harrier, Chopper Gunner (in levels like wasteland where if you get a chopper gunner your team has won)
However, I understand this doesn't work for everyone. If your a more modest player ~ 1 k/d chances are you'll level faster by specifically chasing down certain challenges. For instance if you want to level up scavenger use things that have good synergy. This seems a little abstract but I'll quantify it a little here.
If your working on Scavenger, your going to have nearly unlimited equipment. Use this! Use grenade launchers, claymores or grenades, and throw flashes or stuns when ever your alive. Remember, if you die with any of these still in your inventory you've wasted them. But now your working on Scavenger, gun kills, claymore kills, grenade launcher kills and stun or flash challenges. Often by choosing strong synergetic (is that a word? Oh well) perks you can boost your experience gained significantly. Once you've gone pro on that perk, mix it up with some other synergetic perks
Things like UAV, Care package, and Predators are good ways to work on your kill streak challenges while providing a good advantage over your opponents. Plus, if your not the strongest player you stand a significantly better chance to get these then say if you put nuke on. Even if you get a nuke at some point and you feel like a god, it's still peanuts compared to if you had a UAV up every time you were alive. If a UAV gets you a single extra kill, you just increased your K/D by 1 + how every much your next killstreak just got you. The difference between good players and pro players in Call of Duty is usually a bullet or two. Lower kill streaks are BETTER. Even with a 5 k/d I still find UAV more useful then Chopper Gunner in most games, because I'll get it every time I'm alive.
Hope this helps
P.S. and double xp weekend doesn't hurt either ;)