Hi Rhademes!
Firstly, congratulations on getting in! I suggest that for all the official details on accommodation you check out
this - that'll give you a lot of the information you need.
Personally, I found the application process quite straightforward - the uni should contact you and let you know when you should be applying, especially as an international student. As you've got an offer of a place, you'll be guaranteed accommodation for your first year.
The way Nottingham's accommodation works is that all first-year students live in halls of accommodation: you choose either catered halls, where you have all your meals provided, or you choose self-catered which means that you buy and cook your own food, and live in a flat with a few other students. So the first step is to decide which of these you would prefer. You then need to decide which type of room you would like (again, see the link above for the different types, e.g. single study/large single study/en-suite, etc. Try
this link) There are LOADS of options, so do some good research into it! If you're studying law, then your lectures will probably be on University Park campus, so I expect the most covenient for you would be either catered halls on UP (there are 12 to choose from) or Broadgate Park (self-catered). They're all between 10-20 minutes' walk from anywhere on campus!
Your next step will be to apply online - as I said, the uni are quite helpful about this! Applications open on 1st March and close on 1st August, but the sooner you apply, the more likely you are to get the choice you want. As far as I remember, you list a few options in order of preference, and then once they've allocated the rooms they'll make you an offer, which you need to accept. That's all it is really - after that, all you have to do is start paying your fees. If you need help financing your accommodation then contact the uni.
Hope that's helped - good luck! If you have any more questions then fire away