First of all, don't worry, please don't worry.
A psychiatrist is a well trained professional. They should be aware and sensitive to your troubles. It should take place in a clean and comfortable room.
The psychiatrist will ask you questions relating to your mental health obviously.
First though you may need to give them a medical history, just a very brief one, of any chronic heath conditions you have. To know this information is very important for the diagnosis and treatment of your depression. I you don't have other chronic health conditios thn don't worry about it. You should also be asked what medicatons you take, when you started taking them etc.
If done correctly it should be a relatively lengthy discussion (it's hard to put a time frame on it, but at least 30 minutes). You shouldn't need to fill in any questionnaires as such, everything will be kept verbal. There may be exceptions to this though.
Edit no 2 - If you do clam up then the psychiatrist should give you some time to collect your thoughts. If you still can't answer then just let them know. They really will understand. Just be honet.
You will be asked a lot of questions. Don't get too hung up on the detail, just give as much informatio as you can. Always be honest though. These questions will usually revolve aroun your mental state. Obviouslly the doctor will need to know when you started getting depessed, were there any reasons for the depression (was it reactive - caused by an event). You'll be asked how severe your problems are and possibly if you have any suicidal thoughts. You'll also be asked if there's a history of mental illness in your familyand whether you abuse drugs or self harm.
At the end of the appoitment the psychiatirst will give you a diagnosis or, if there are complicating factors, ask you to come back for another appointment. A care/treatment plan can be offered depending on the severity of your illness, this will usually new or a change of medication, cognitive behavioural therapy, counselling and continued appoitnment with a psychiatrist and, eventually, if you start to revocer, close monitoring by your GP.
Don't get too worried. The psychiatrist will be sensitive to the fact that you're very nervous about his, particularly if you have social anxiety (as I do). THey should make every effort to make sure you are kept comfortable.
Take care.
Edit: - I can't say whether or not the assesmnt will be recorded or not. It shouldn't be, the psychiatrist will write donanything that he or she needs to. If it does get recorded, or somebody else need to be present during the assemsement,they will ask for your permission. This shouldn't happen though, so don't worry. If yo do feel s if you are being fobbed off or ignored (I know the feeling) you are entitled to ask for second opinion.