How do you find better stuff on fallout shelter, does it involve luck or something?
Yes, a vault dweller's Luck stat plays a large role in loot quantity and quality, but time-in-the-wasteland also is important. Loot quality apparently improves with time outside the vault, and the longer they're out there the more items they will collect. There may also be other factors not immediately obvious, as some vault dwellers will consistently find more loot than others even though they all have maximum Luck stats.
What I've come to realize, the game itself says, and is not mentioned in the other answer is: The amount of time the Dweller spends in the wasteland.
The better armor and weapons and more medkits, and rad-aways - the more time a dweller can spend in the wasteland - the better loot he'll find.
If your dweller's stats are maxed, and their level is around 35+, you can leave them out there for a few days at a time. Be sure to equip them with 25 stimpaks (max allowed) and 5 radaways, and also a decent weapon (10+ at the very least).
Each time they level up out there, they'll get their health refilled, which helps them to last for a long time. Eventually you'll start to get some nice stuff, although it really is random, and sometimes they need longer than other times.