Make sure you've read the plans for your item. To read them, go to your PIP-Boy, and then choose Items > Notes. Sometimes a plan is an aesthetic "skin" for another item which you must also own.Â
Some items won't show up if you're inside a vault because they can only be constructed outdoors.
If you purchased something from the Atomic Shop, you may need to exit the game (or the shop) and then return for the item to appear.
Visit The Dutchess Flame's article on how to purchase individual Atomic Shop items using atoms directly from Bethesda's website. Her article is at https://www.theduchessflame.com/post/how-to-request-items-from-the-atom-shop-for-fallout-76
Look for user Angry Turtle on YouTube for all sorts of useful tips.
Reddit is your friend.