As you've asked this on the UK board, this reply assumes that you're based in the UK.
Firstly, there's an awful lot of red tape.
You need to register with DEFRA to obtain a holding number. You need your holding number because when you buy (or sell, or even move) your cow, you need to notifiy the British Cattle Movement Service. This information ensures that her passport is kept up to date.
You will also need to infrom you local Animal Health Authority because there are compulsory TB tests in the UK. It doesn't matter that your cow is healthy, these tests have to be done regularly (the testing interval is between one and four years, depending on the 'risk area' that you live in).
You will also need to have your cow tested for Brucellosis every two years (although this scheme might soon be ended).
You will need a securely-fenced grazing paddock of at least an acre - if you have company for your cow (which you really should as she is a herd animal and will be lonely on her own), you will obviously need a larger paddock. A regular water supply and shelter goes without saying. Plus a good supply of winter feed (hay/silage/fodder beet or potatoes and a grain meal)
You will need handling facilitles (at least a 'crush', preferably also a 'race') to handle your cow safely for veterinary treatment and her regular testing.
Your cow will need milking at least twice a day, every single day (including weekends and holidays) or you will have a serious welfare issue on your hands. You are also likely to have a serious milk overload problem on your hands as well, unless you intend to make your own butter, cream and cheese as well as just using the milk as it comes.
Again, assuming that you are in the UK, you can't sell your surplus milk at the gate unless you have the relevant hygiene certificates.
On top of all this, there is more documentation needed to record movements, treatments, calvings plus some way to get your cow in calf (you need to take her to a bull or bring him to her), veterinary treatment as and when needed, and last but not least, commitment.
Not all cows take easily to hand-milking, so you might well need to have perseverance, patience and a strong constitution because your cow will probably weigh around half a ton. If she isn't co-operative you need to be able to take some knocks and stand up to the bruises, although proper handling facilites (as mentioned above) will help minimise physical trauma to yourself.
If you want all of the milk for yourself, you will need to take her calf away and probably sell it. Failing that, you will need to share her milk with her calf, although this has obvious health implications.
Which brings us on to buying a milk pasteurising unit.
Buying your cow is a further issue, but really is the least of the problems you're likely to encounter.