Any of the ideas I'd said above wouldn't be solo operations. Sure they could be but finding a friend to be your business partner or creating a small organization to manage and run things both helps manage risk but also helps fill in the gaps in your own skillset.

The easy option is just to talk to the local library about running a film festival, get it scheduled in the community room and put on the library events calendar and just bring a laptop and a projector if the library doesn't have one and watch some public domain films. This can grow into a larger indie film festival in time and in the short term you can get your feet wet and have some fun doing something meaningful in your community

Now if you wanted to go all out and do it for real with an actual budget (still only talking single digit thousands at the most though! I know folks who spend that much annually on their private hobbies, and if you play your cards right you can probably break even pretty easily) and really try to make something of the whole thing, this would be my gameplan if I were to try to set one up in my town:

1. Enlist some friends/trusted family members to help run it, create some loose organization amongst your enlisted folks to help delegate tasks and share the responsibilities and costs, create a regular meeting/working session schedule and break out into task forces as needed
2. Look around your local community and identify potentially suitable event spaces. Is there a local art gallery or community center you can rent out? Maybe an indoor/outdoor space at a park you can rent out from the city? What's the cost to rent it out for an evening? How many people would be allowed in the space at once and what would it take to setup a projector, some speakers and a laptop?
3. If you find a suitable enough space and have reached this stage, strongly consider officially registering your organization (a non-profit would probably be lowest-risk since businesses and governments love donating to non-profits and it makes it much easier to rely on volunteer labor and donated hardware and licenses further reducing risk) this is also the stage where you should have ideally identified your budget and general gameplan for running this thing
4. Consult your local government and any local colleges for assistance. See if you can get any film, culture, English or even just liberal arts instructors on board with helping boost your event. Your city government may have resources they can offer as well, since boasting an indie film festival is usually a good thing for any city. This is one instance where living in/basing your operation in a smaller town is a big benefit because the local government will likely be excited to help however they can to build more local culture and draw to the town.
5. Schedule it! Book your reservation of the event space
6. Advertising! Post fliers, ensure its mentioned in the local paper and local news (if they exist) make sure its listed on the events schedules that would be relevant. Get any local/regional colleges aware of the event so that students might come attend. Contact the senior centers and make sure you're on their event calendars so you get some bored retirees to attend too
7. Get your equipment in order. If you went the non-profit route contact local AV/IT companies for donations of equipment/time. Many of these companies will donate both in exchange for plastering their company name on event as a sponsor. Also get your food vendor(s) in order. See if there's a good spot for a food truck to setup shop and contact some local food trucks to gauge interest. This is also the stage to line up your tuxedo rental so you can look the part when you give your opening/closing speech about how proud you are to have seen this event come together
8. Run the event! This is probably the hardest part because everything you thought would be fine will go wrong, while the parts you thought would catastrophically fail go perfectly, but ultimately its fine because its a brand new indie film festival and nobody expects it to have the polish of Sundance or the Grammys.
9. Do it again the next year! Or even in 6 months! Once you've held a couple of festivals you'll start collecting some regular attendees, made some extremely important contacts, and you'll have started to establish a reputation. Maybe this is just a cool thing you do now, or maybe it grows into an actual big thing! (if it does and my comment inspired you, please let me know though! I'd love to know if my random brain dumps on weird corners of the internet actually impact people in meaningful ways!)