I assume you're shooting 35mm, right? If so you need chemistry, a processing tank and reel, a bottle opener (for opening the film canister), and a changing bag to open the film and load it on the reel in, and possibly a water bath to control temperatures (definitely needed for color). Oh and a thermometer. No darkroom required for processing film as you're handling the unprocessed film inside the changing bag.

For 120/220 film, omit the bottle opener as it is not needed.

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