Developing your own 35mm or 120 black and white film is a fairly simple, satisfying process but you need to closely follow the developing instructions for the type of film you are developing. Times and temperatures will vary from film-to-film and developer-to-developer.
There is no need for a fully equipped darkroom to develop film but you will need to load the film onto the reel in darkness.
Most people will use a loading bag such as the Paterson changing bag ; a dark material bag large enough to fit the developing tank, reel, film, scissors, bottle opener and your hands while keeping any light out. Use the bottle opener to release the end of the film canister. The film will be taped to the inner reel. Cut the leader end so it is straight across. If you have a room that can be completely closed off to any light this will work too. No stray light can be allowed to seep in.
The Paterson Universal Tank will accomodate 35mm or 120 film on the same adjustable auto-load reel. This type of reel makes film loading easy in the dark. Once loaded and lidded the tank can be brought into the light. Liquid is poured into/out of the light baffled top of the tank.
A dial-type thermometer is essential to monitor the liquid temperatures for developing film accurately. Temperature can affect contrast/density of the developed negatives. Developing times/temperatures can be found on the inside of the film box or by searching online.
Chemicals needed for development are developer, stop bath and fixer. For an easy starter kit including pre-measured packets of all of the aforementioned chemicals try the Ilford Simplicity Film Kit
A wetting agent such as Kodak Photo-Flo is also recommended to prevent spots forming in the drying process.
More chemicals in larger amounts can be found here Film Chemicals