fastest Way to Level up on Fallout 3.  

First off there is a perk you can get 3 levels in that raise your experiance by 10% each time. It's called Swift learner and you can get a make of plus 30% boost from it. Also well rested adds another 10% which is when you sleep in an owned bed. And you can make the difficulty harder again to get more experience, not advised if your new to the game though. That's to start out.

when you sleep in your bed or a hotel bed you get an expirience percentage boost. Also do all of the side quests they give a lot of expirience. That's how i got to 20 and if you get broken steel collect super mutant blood samples they give 10 xp and like 20 caps each. Also i went for good the first play through because i wanted a place in megaton and the second time I went for evil because i wanted to see a nuke explode. Theres also some glitches you can exploit but i only found them on the xbox and i dont know about the playstation.