Huge subject, and I'd highly recommend you read up on the subject first, but a very basic resume'.....
Basic requirements..
Devoloping tank.
To be loaded in complete darkness. Practice with an old film a lot before you try the real thing.
Chemicals.
Developer, Stop Bath and Fixer.
Measuring beakers
One for developer, stop bath and fixer, unless you wash very thoroughly between baths.
Trays
Three - one for each solution... the larger sizes get expensive!
Photographic thermometer
Essential IMO.
Darkroom safelight with orange Filter
Provides enough light for the printing process.
Enlarger with lens
Well... you just need one.
Printing paper.
There are plenty of other bits and pieces which will make life easier but the above are the bare essentials.
Developing the film is by far the most critical bit as you only get one stab at it. Read the leaflets which come with your chosen chemicals - they'll contain all the info you need, but you need to have a very good idea of what you're doing and your work flow before you start.
Maintaining a reasonably constant temperature throughout the developing process is a bit Heath Robinson in your typical home environment. Get your chemicals to your chosen temp, then stand the tank in a larger bowl of water to which you can add warm water as required to keep the temp constant.
Be scrupulously clean about washing everything when you've finished. these chemicals can dry out and become crystalline and airborne, badly contaminating a room with the result that mysterious brown spots start to appear on your prints.. not to mention the health implications.
Printng and enlarging
Great fun and everyone should do it, but once you've experienced the dust spots and hairs etc on your prints, you'll really appreciate digital processing.
I'll leave you to experiment with the printing bit , it's far too big a subject to tackle here.
Just a thought, but why not go for slides instead? Once the film is in the tank, the whole process is carried out with the light on and is effectively finished once you've developed the film. As long as you use E6 film you can get a home procesing kit of chemicals from Jessops et al. Scan the slides into your PC and you have all the advantages of digital editing, the fun of using film, but without a lot of the time and hassle.