Traps and snares work well, and have worked for thousands of years. That being said, lets be honest! This is hard work and you have to set up lots to make it even remotely a possibility you will catch anything, but with out a firearm this is pretty much your only option.
If any thing from my posts please learn how to set snares and traps, you never know when you will need this knowledge. Learn all 6 below
(Picture Credit: theprepperjournal.com)