There are a ton of people in the martial arts/self defense space with a lot of knowledge who still want to teach, but don't have their own schools with a storefront. They teach often on a non-regular basis, out of their garages or backyards and with little concern for money, some to get extra money on the side. Some of my best instructors have taught me for free or cheaper than if I went to an actual 'school'.
Usually these guys are serious about what they train. They're not doing it for money and are doing it usually to spread their knowledge. They're interested in other people who are serious about training too. You have to go in with the mindset that you really truly want to learn something.
CraigslistSeek people out on craigslist in the community section. I recommend both browsing and posting. When posting, just be honest about what you want to train. I personally found one very good instructor this way in Austin, TX.
Your own networkAlso, ask your current martial arts contacts. Lots of people in the martial arts world have been doing what they're doing for awhile and likely know people who teach or would be willing to teach for free or cheap. One of the guys I learned the most about Kali from I found in Springfield, IL this way.
GroupsGroups like ARMA and the SCA teach/train in a group atmosphere. I've met other small martial arts groups that train this way too.
Don't do any of what I just saidI really don't recommend you do this until you've been studying at least one art for a little while and kind of know what you're getting into and what you should be looking for. I highly recommend you do not start this way. You need to understand the space first and you need to get at least some very basic safety instruction from undoubtedly-qualified people. You should know how things are supposed to feel, otherwise you won't be able to assess for yourself just what is safe and what is not and who is an asshole instructor and who is not.
Again, be vigilant and verify credentials all you can - it will save you.