Scrapping items is relatively simple. This achievement is going to be a bit of a grind, though.
After playing for a while, you will have acquired some weapons or outfits that you just don't want anymore. You can either sell them for Caps or scrap them for a chance at crafting items. This achievement is for scrapping, but both functions can be found in the Storage menu.
You can only scrap Weapons and Outfits, you cannot scrap Junk or Pets (you monster). Once highlighting the item you want to scrap, you have two options: sell (the cap with the arrow, option on the left) or scrap (what YOU want, the recycle icon on the right). This will be a button prompt on console, or just a click on PC.
Once scrapped, you have a chance at acquiring crafting materials, located in the Junk file of the Storage menu. You CANNOT
scrap items if your storage is full or overfilled, you must sell items or equip them to dwellers before you're able to continue scrapping.
If you want to check your progress, there are counters under the stats page for Weapons Scrapped and Outfits Scrapped. They're located under the "Cumulative Since (Current Date)" header in the Stats page.
In case you're wondering, the first crafting room becomes available at 22 Dwellers, it's the Weapon Crafting room.