In general, it;s just a simple grind. However, there are a few tricks and tips to speed this up.
EDIT - You need to hit level 55 and max it out. After that, you'll be prompted to go to the General in the HQ area and prestige. You can find the entrance to the area with the General in just near the Division Prestige section
1) Play War Mode.
You'll find you get significantly more kills during playing this mode, and easy points from building or demolishing locations in the game. Matches can take anywhere from 4 minutes to 8 minutes realistically, and during this time it's pretty easy to get a significant amount of points. Just remember to build anything you see, or demolish anything that's already been built. Get to know the maps, and what scores you points. Being near the tank in Operation Griffin when it crosses the line in the first phase, for example, will net you a sweet 500 points.
2) Complete challenges.
Weapon challenges are pretty easy to snag, so make sure you're keeping an eye on them swapping out your load regularly to keep them coming. You might be an absolute beast with the Enfield rifle, but if you've already completed the challenges you're doing yourself out of some nice bonus points. Plus, if you're playing War Mode, it's easier to get those kills and level up the weapons you might not be that great with.
3) Contracts, orders etc.
Keep an eye on these, and always pick up the contracts that award bonus Exp. Normally, they are pretty simple ( 100 kills in 40 mins etc. ). War Mode makes these super simple.