Summarize the following:
You will get a notification once the merchant has spawned. Once this happens, go to your house/houses and look for him there. To talk to an NPC, stand next to them and right-click on PC, or press Circle on Playstation, B on Xbox, and A on Nintendo consoles. Place the bug net in your hot bar, and equip it.  Then place the cursor on a critter and press the attack button to catch it. Critters are found all over the Terraria overworld, but you'll want to focus on catching worms, snails, sluggies, fireflies, and buggies due to their high bait power.

Summary:
Talk to the merchant. Catch critters and butterflies with the bug net.