You need:
A paddock, large, clean, well fenced.
Shelter - a stall or stable, or a good quality shed. Somewhere to store the horse's equipment and where it can go if it is cold, windy or raining.
Tack - saddle, bridle, bits, halter, saddle cloth, rug etc.
Horse feed - you'll need hay and if you're intending to ride the horse, concentrates.
Company - horses don't like to be kept alone. Keep two horses, or keep it at a stable or agistment facility where there are other horses. If you cannot have another horse, keep it with sheep, cattle or goats.
Money - costs of feed, shoing and vet care are ongoing and they aren't cheap. Buying the horse will cost about two thousand dollars and you will need plenty to look after it.
I'm going to give you a more thorough answer.
You need to give him a stable to stay in. You should, or your stable should, feed him twice a day, bathe him in the summer, groom him once a day or once every other day, and give him a place to run around outside or exercise him.
As well, you should pay for a farrier, a vet, and maybe a trainer or equine dentist.
Farrier- a person who shoes horses and clips their "toes". Even if your horse can live without shoes, a farrier must visit to trim his hooves so that his movements, his joints, and his bones do not deteriorate.
Veterinarian- Basically, a doctor for horses. It should be obvious why you need him/her.
Trainer- If your horse is 'green' (inexperienced/untrained), then you need a trainer to train him to the point where you or someone else can ride him or do something else productive with him (show him in halter classes, drive him, or even just to perfect him tempermant)
Equine Dentist- Some veterinarians also do this job, but many people are relying on trained specialists to deal with this. The equine dentist files down horses teeth so that do not become pointed due to eating grain. If a horse's teeth become pointed, then he/she will not be able to eat as much and could lose weight, and if not cared for, could die of malnutrition.
I know this is a lot to take in, but owning a horse is a large responsibility.
Also, after all of this, you must keep in mind some other things...
Deworming- Horses are very very susceptible to different parasites. Deworming them makes it so that they do not pick up these parasites, and if they have them, this will kill them off. You need to deworm your horse approximately every three months or so.
Shots- Horses, especially older ones, can bring in a range of shots. To get more into this, if you plan on buying a horse, talk to your veterinarian, or the person who runs your boarding barn (if applicable)
Extras: Horses are expensive. Ive composed a list of materials you will need to ride your horse, just basic riding (trail riding, ring riding).
- Bridle (including reins, bit, actual bridle piece)
- Saddle (Including girth, stirrups, and girth cover if applicable)
- Saddle Pad
- Halter (Don't turn the horse out with it unless it's a specific "break-away" halter!)
-Lead Rope (Never drag on the ground. Just don't!)
Not to mention the odds and ends (just a few here, there are many more...)
- fly spray for summer - a crop if necessary - grooming supplies (there are many more, but these are the bare essentials)
- Hard brush
- Soft brush
- Hoof Pick
- Face Brush
- Curry comb
- blanket for winter
- Wraps and first aid for "just in case" situations
For yourself, if you don't already own (I hope you do. Don't ever get into buying horses unless you have ridden. It just isn't smart.)
- Breeches or Riding Pants of some sort
- Helmet (not necessary everywhere, but I believe all riders should wear one for their own safety)
- Riding boots
Horses are a very large responsibility. Please be safe and don't buy a horse unless you are extremely sure that you are ready.