Just use double xp things from battle packs and play tdm or something and do good

There is no really good boosting methods that i know of but the best way to get exp is when you do the following

1.) XP Stacking - You know those XP boosts you receive in Battlepacks? Save those bad boys for a double XP weekend. They stack!

2.) Party Up and Play as a Squad

3.) Plug in That Mic and Use It - Communication is key

4.) Do Your Classs Job, and Be Flexible - if someone needs ammo and your support GIVE THEM AMMO [easy exp]

5.) Suppress fire equals extra points

6.) Spotting bonuses

7.) Be Your Squads Spawn Point - Either stay alive alot or use a spawn beacon

8.) Give and Follow Orders - get points when orders are executed

9.) Work for Medals or Assignments - those two are your best friend not to much points but they add up quick

10.) Plant Bombs and Secure/Defend Objectives (PTFO) - Dont just go for kills be sure to play the objectives of the gametype

In BF4 boosting is pretty difficult to do
Assignment boosting is relatively easy but if you are just looking to kit boost. You might be looking for a while.

Kit boosting is relatively difficult because nobody is willing to die 60 times in a game just so you can finish off your assault kit. However, if you can find someone to do this with..you will actually need 4 people so the game will start. Regardless, here is how to boost in BF4

1) Join a Rush server with nobody in it.

2) Make sure you have 4 people and that your partner is on the opposing team.

3) Have your partner spawn in as a Recon kit with the radio beacon (you will need to have
already unlocked the radio beacon before boosting)

4) Bring your partner to one of the MCOM sites, the other group of 2 should goto the other MCOM to avoid confusion.

5) Have your partner place the radio beacon close to the MCOM stations.

6) You may then start to kill them, have them respawn on radio beacon, rinse and repeat.

The MCOM station will give you some bonus XP. That will help you rank up a little bit faster. If you are interested in XB1 boosting, send me a PM and I'd be more than willing to help out as I know finding boosting partners on this game is much harder than in BF3.

Hope this gave you an idea of how boosting works in BF4