Best to book at appointment, then when you turn up they give you a folder to read which explains the process, and a form to fill in just checking all the things that might get in the way of donating. Then you wait a while, get called up by a nurse and have a preliminary test/interview where they'll go over your form and take a drop of blood (pin prick on end of finger type thing) to test for haemoglobin levels.
Then you wait around a bit more before being called to a doctors bed thingy, you lie down and put your arm on a cradle type thing. The nurse cleans the area on the inside of your elbow and puts a cuff on the top of your arm - you'll be asked to clench your fist, which together with the cuff makes the blood vessels stand out easily. They then insert a needle which is usually less painful than the initial pin prick to test for the haemoglobin, although it depends on the humidity in the room really - if it's humid then the alcohol swab doesn't evaporate and it stings a little bit.
Then the cuff is removed and you'll be asked to slowly clench and unclench your fist. Continue for however long it is - can't remember, but I'm doing it again this friday so can get back to you if you like - basically they fill up a container. They'll check on you a couple of times if it's your first time. Then when it's done they'll remove the needle (don't feel anything), and ask you to press a cotton ball to it firmly. Then this will be taped to your arm to stop the bleeding. You might be asked to sit half-up for a few minutes. Then very gradually sit right up and dangle your feet over the edge for a few minutes. Then eventually a nurse will accompany you to the drinks/food area, where you'll be asked to take it easy and drink some cold squash - tea and food is available, but not recommended especially for first timers. After a good 5-10 minutes of sitting around, you'll be allowed to go.
I didn't really feel much from the loss of blood first time - if anything it relieved a slight headache I had
Sometimes you feel a bit light headed - like after a quick strong pint.