Get your farm to build up a little stock of sleep herbs and parashrooms. You can combine those to make tranquilizer, which you then combine with bomb casings (stone + sap plant) for tranq bombs. Alternatively if you don't want to invest that farm-time, you can just buy Tranq from the store that way.
For home-made traps, you have to buy trap tools from the shop and combine it with either a net or a thunderbug. Thunderbugs can be farmed, but they're a pretty high resource cost, you'll mostly be doing a lot of venturing out with your bug net (which also helps to get you spider webs, a component in net-making)