In Don't Starve: Shipwrecked you can build a variety of traps to catch birds, bugs and other creatures to use as bait or for food. To build a trap you must collect the correct materials, such as twigs and grass, then assemble it on the crafting screen. Once the trap is built, just tap and drag it from your inventory and place it wherever you want on your world map.
Baiting traps is not necessary to catch something, but it helps. You can use a variety of things as bait, like dead crabs.
You will know when you have caught something when the trap is closed and bouncing around on the screen. Just tap the trap to collect whatever critter you have snagged.