New Kid(Bronze)
Reach 10th level
As you are playing the game you will earn EXP points for pretty much everything you accomplish. You will earn EXP for killing enemies, mutated insects, abominations, mutated animals and robots, finding new locations, completing main and side missions and more. If you take the Swift Learner perk, you can speed up your leveling. The Swift Learner perk will give you plus 10% per level that you choose the perk on whatever the experience is you would have gained. There are three levels of the Swift Learner for a total of 30% extra you can add to all the EXP you gain. Once you hit level 10 this trophy will unlock.
This goes for the first 3 trophys as the other 2 are Reach 20th level and 30th

Crafty(Bronze)
Craft 20 items
Crafting is something that has been in the Fallout series for a while and they made this trophy very easy in this game, unlike in Fallout 3. For this trophy you must simply Craft twenty of anything. The quickest way to get this is to pick up any Empty Energy Cells you find. Your first Workbench is located at Goodsprings on the side of the General Store. Head over to it and Craft some Ammo, or recycle your Energy Cells and you will get the trophy as soon as you hit 20.