Renting Privately.
I basically don't have that much knowledge of renting privately because I managed to get my flat quite easily but I will say what I know.
Renting privately can turn out more expensive or cheaper than halls, depending on where you look. The centre of town is around £500 per person per month excluding bills (although there will be the odd cheap place in the centre.) The further out you go, the cheaper it gets but you'll struggle to find much below £250 per person per month. Choose a realistic budget. Remember you still have to pay bills on top of your rent in most cases. Being out in the badlands is not the end of the world. St Andrews is a small place and even being on the outskirts of town is still only about 25 minutes from town!
Getting a house/flat in St Andrews is difficult and you need to be prepared. There are various estate agents around town. The most popular are Premier Lets, Eve Brown, MDDC, Bradune and Co, Pagan Osbourne and Inchdairnie but there are others. You need to check their websites/go in and ask around January time and make a list of when their lists of properties are coming out. You need to be prepared. Get up early on the day the list is released and go queue. You'll need references (a character reference and one from halls. You'll need to sign up to a list to get this from the warden and it might take a while to complete so get it organised early) and sometimes a few other things (check with the estate agents before the list is released). Once you get the list, go and see the flat and apply straight away.
After that, you may be interviewed. They'll ask things like how you met your flatmates and what your hobbies are etc. Be prepared as you want to give a good impression because it is very competitive. After that you'll either get rejected or accepted. Apply to as many flats as you can and a wide range of them. Not just the cheap ones in the town centre because they are the most competitive. Go a little bit further out just so you don't end up having nothing.
A few other ways to get a flat is to make friends with 4th years who are leaving or anyone else who is moving out as they can then tell their landlord about you and you'll get a flat.
Or try uni managed accomodation. Though please be aware that these houses are really really competitive and are choosen by random ballot so it is purely down to luck. and you can't apply back to halls if you apply to one of these. Applying back to halls is a good idea just incase you don't get a flat. You can always turn down the offer.
This guide has some really great advice in regards to private accomodation. Please read it!
http://www.yourunion.net/studentvoice/content/7757/accommodation/how_to_rent_201011/