This one took me a little while to figure out, but now it’s just so simple.
When you want to catch a particular Onigo (assuming it’s one that you’ve already encountered once before), just check the Catalog and find that enemy’s entry:
Examine the “Capture element” and “Capture size” entries. (In this case, it’s “BST” and “Small”). Also, if you’re not sure where to find them, check the Location(s) at the bottom of the screen, or the “General appearance area:” on the top right.
Now, when you’re in that location, click on “Traps” and go to the “Set trap” screen. Choose the size of the trap (which should match the “Capture size” for the Onigo), and then choose the Bait.
The Bait MUST attract the “Capture element” of the enemy you want to trap (in this case, “BST”).
Now “Set” the trap, and when the timer’s up, you’ll get a notification that the trap is full, and you can click on the “Traps” icon again to go straight to the trap.
When you defeat enemies that are caught in a trap, you automatically capture them.