I'm going to take a risk and assume you mean shooting 35mm film for a motion picture. Your least expensive option is likely to rent an ARRI 235 or 435. I have seen the 435 for as low as $250US per day. That price does not include the PL mount lens(es). A single roll of Kodak 35mm Vision 3 will run you more than $300. Adorama has Foma Film Fomapan 400 B&W for $55US per 100 foot roll, but it is currently on back order. AND it's black and white film from the Czech Republic. You can occasionally find new old stock 35mm film on ebay, but beware and only buy from trusted sellers. THEN, even after you've shot your film, the cost doesn't stop there. You have to send the off to be developed. That is charged by the foot. After you get your developed film back, you have to edit it. If you don't have access to a Moviola, you will have to find someplace to edit your project. As you can see, renting the camera itself is the least expensive part of this process.
The only trick is that the cameras often rent cheap because rental houses have them laying around collecting dust (sometimes literally). You can also get good deals on stock & processing - again because it’s not used as often anymore; I’ve worked with DPs who get good deals because they commit to using film on a majority of their projects (so it’s beneficial for, say, Kodak, to give them a discount on stock).
But it’s far from cheap. If you keep your shooting ratios way down and get half-decent deals, you might be able to get it to a cost on-par with something like a full Alexa production kit & DI, but maybe.
I don’t know where you are but you can call your local (if you have a local one, you might need to venture out further; for a while in Australia we had to ship film to Asia to get processed) film lab to get an idea of cost. Work out your shooting ratios to get an idea of your stock cost. Camera bodies are cheap to rent but you might find lenses aren’t - because they can be used on modern digital cameras.
So true. If it's just the "film experience" you're after, there's always Super 8. You can buy a Super 8 camera, film, and processing for less than a day's rental on a 35mm camera. There are loads of cameras on ebay for less than $20.00. I even found a beautiful Yashica with the 12-30mm f 1.2 lens for $14.99 with $9.99 shipping. Super 8 film is still available and processing costs less. 50 foot rolls of Kodak Vision3 can still be had for $30.00 or less. Editing can be done on an inexpensive home movie editing unit. I have found units that will splice both 8mm and 16mm for less than $20.00 on ebay.
There are no tricks using this method in the digital era. As others have said, camera rental
is less expensive than in the past but buying film and processing is still expensive. The nice
thing in the digital era is you can transfer the footage to digital for editing - and that saves
a lot of money.
You don't offer much info from your end. Do you have any experience shooting film? Do
you have a DP who shoots film?
Work with someone that owns a kit. In other words if you find a DP that owns, you don't have to rent. They will likely charge a kit fee but it all depends on your situation. Perhaps your project attracts them or you can offer something back.