Search every container, use vats to make sure you dont miss, I normally use melee when i can as it saves so much ammo!

As others have stated loot, loot, loot. Think of it as a scavenger hunt I explore every location I can see on my had one my way to a quest marker and if enough ammo was not accumulated with that I spread out and find more buildings or towns. But be careful ghouls and super mutants take up some ammo aswell, and for a new fallout/elderscolls player turn the difficulty down until you get used to it, you can do that in the options menu!

Hope I helped,
Kuuuush