Fallout – Level up quickly in fallout 4

You should try to get the right skills to level up faster:

1. Max out your Intelligence to get more EXP per level (Alternatively you could upgrade your luck to 5 and the skill Idiot Savant to get randomly more EXP the lesser you Inteligence is. But Intelligence has to offer some usefull skills, so I wouldn't make it that way.)
2. Upgrade the skills Locksmith and / or Pickpocket (you'll need Perception), Hacker (you'll need Intelligence which should be at 10 because of 1.) and Charisma to persuade the people. Each successful event will give you EXP (and some loot). You don't need level 4 of Locksmith and Hacker.
3. While this will take some levels (regarding your starting skilling) you should explore every point of interest on the map. On your way you can use the skills from 2. and kill some monsters.
4. Also try to collect many materials for building weapon or armor improvements (therefore you could also increase the skills Armorer and Blacksmith (level 4 and 5 of strength), Gun Nut and Science! (level 3 and 6 of Intelligence)
5. Thanks to nickson104: Build things in your settlements. Collect Ressources to use them at the workbench.
6. And of course: finish as many side and main quests as possible.

Hopefully I mentioned everything. You could give this side a try where I already have choosen a good basic skilling for your case.

Killing big monsters isn't the thing. They are really hard and don't give you the EXP which is worth your ammo and / or stimpacks.

Good luck, wastelander!