Just choose a clinic, and then decide whether you want to use a drop-in service, or if it would be more convenient for you to make an appointment.
At mine, I use my real name and give them my GP's details etc., but you can tell them not to contact your GP. I think at others all you need to do is give them any old name and a mobile number for the results.
It's fairly quick and painless, don't worry! But wait two weeks if you think you might have been potentially exposed to something, re. HIV detection - earlier obviously if you have any symptoms.