I think it's expensive. Extremely expensive in relation to wages. Third most expensive in the entire UK, in fact, outside London - where people get a London weight added onto their wages - and Bristol/Bath.
The rents and council tax are steep as well. Expect to pay at least £500+/month for a two bed place. Unfurnished. Around £400+ for a one. Not including council tax, which will go up another 5% next year.
The vast majority of housing is in the form of 4 and 5 storey tenement flats, very few of which have lifts or off-street parking.
If you're applying to Edinburgh University as an undergraduate, you use the UCAS system, as just about every other British university does. If you are applying as a post-graduate, contact the college in which the department falls - Moray House School of Education for the PGCE programme, for example.
The university's population is about 85% English and quite affluent in its makeup. Whilst there are mature students in some undergrad programmes, they aren't as numerous as at other universities in the area, like Napier or Queen Margaret.
For fees info, check the Registry website. The general 3+ years previous residence in the UK to qualify for home tuition applies for the most part, however.
www.ed.ac.uk