Good lord, tough crowd here.
I attended the OASB twice, unsuccessful the first time and got through the second time around. I did attend around 12 years ago now so some things may have changed a little bit but probably a good start.
You report to the OASB and are given a rough tour of the base and where you can find things over the next couple of days i.e. Food, Relaxation and Bed. You are then left on your own with the others in the group to 'get to know' each other and told to report the next morning nice and early.
On report to the classroom you will be met by normally two Officers who will be your assessors over the next two days of exercises. Both my OASB's started with going around the room giving a quick introduction of yourself. There was then some classroom based group exercises that consisted of some 'scenarios'. They will give the group a laminated card with a scenario that will require some group discussion and debate to be able to come up with a solution. The assessors will just sit back and watch how everyone interacts and works together. At the completion of the allotted time the assessors will then ask 'random' questions and critique your suggested solutions.
In the afternoon all went outdoors for some challenges, we were split into two groups and someone from each group was appointed 'leader' then given a briefing card with a scenario. It will be along the lines of , there is a canyon you need to cross and you have two planks and a piece of rope to get the whole team across. You have 10 minutes to plan and then 10 minutes to carry out the exercise. You will go through lots of these to give everyone a change to be leaders. Once again the assessors just observe.
The next day there was more classroom work including impromptu speeches where you pull a topic out of a hat and have 5 minutes to prepare a 2 minute speech which you deliver to the class. Also and individual exercise where you are each given another 'planning' scenario to work out an answer to. You then have to go individually with the two assessors to give your solution and explain how you came up with your idea.
Finally in the afternoon a round of interviews with a psychologist and then a couple of Officers. You then sit around for a couple of hours whilst they discuss everyones rankings. You then get called in to have a debrief with the Officer in charge who tells you if you have got through. If no you pack your bags and go home, if yes then you stay another day and have a medical carried out with a number of specialist tests, chest xray etc.
My advice is just be yourself, brush up on basic maths as they quite often throw in questions like 'so at 20 km per hour' how long will it take you to cover the 38 km between bases in your planning exercise etc. If you don't know the answer to something just admit that you don't know instead of winging it. Finally practice your public speaking and have a thing about the group exercises, plenty of books available on the subject, generally DON'T be the guy talking all the time, make sure everything you say is contributing and you are not just making noise. And finally keep updated on current affairs as there will be an 'essay' question at some point which will ask you to write about a current topic in the news. Mine was the advantages and disadvantages of MMP.
As I say it could have changed in the last few years but just be yourself.