hi im currently in halls at kings so i can try and answer your questions.
after you accept an offer they will send you a booklet with details of all the accomadation with prices and some pics and stuff in. you then apply on the internet and rank the properties in preference order, they reccommend you rank all of them as not that many people get their first choice and some will get like 6th choice or something.
Im at great dover street apartments (my second choice) and they are basically separated into 10 blocks with 5-7 floors in each. each floor has about 2 separate flats with 4-9 people in who share a kitchen. you all get ur own ensuite (its about the size of an aeroplane toilet tho!) in total 750 ish people live here and its about 5-10 mins walk from guys campus, 25-30 walk from waterloo and 40 mins walk to strand.
stamford street apartments are the same layout but just across the road from waterloo campus, these are really popular cos of location so don't set ur heart on living there.
there is also Kings college halls (KCH) which are out in denmark hill, these are more traditional type halls with corridors of rooms and shared bathrooms and are catered. they are a lot cheaper thoand they have more social events and their own bar but are furthur away, bout 35 mins bus to waterloo i think.
hampstead are self catering halls bout 35 mins tube to waterloo (in a posh area)
theres also intercollegiate halls which are around russel square (v.central) these are mostly catered and you will share with UCL, LSE etc students so its cool you get to meet loads of different uni people and go to their union events with them!
hope that helps a bit, i can try and put up a few pics of gds if u want?