Get a haircut - slightly longer than the military fashion. Get it cut shorter the next time you visit, it gives the impression that you've learned something already.
Take money. You should be invited into the bar afterwards and beer tokens make instant friends. If you're not invited to the bar, find another unit.
Wear leather shoes and shine them before you go. They don't need to be mirror finish, you just need to show that you've got an interest in your appearance. Don't wear shoes with slippery soles, especially if the TAC is an old Drill Hall with a polished timber floor.
No need to wear a tie unless you're hoping for a commission, but if you wear a pullover, wear your shirt collar on the outside (unless you're wearing a tie).
Dye your hair back to its original colour (unless its ginger) and remove any visible piercings. A Prince Albert can be left in until the Medic tells you to remove it - this will provide humour for the rest of the people at the medical (this will be on a subsequent occasion).
Before you go, make a list of the questions that you want to ask. Copy them into a small notebook and take it with you, together with a pencil, sharpened at both ends. Take notes.
Tell your mum/wife/girlfriend not to wait up (remember to take your doorkey). I strolled in at 4am after my first visit.
Don't chew gum and don't put your hands in your pockets (except when visiting the bar).
And enjoy yourself. If you don't already know anybody there, it can be a bit daunting. It will be confusing at first as people mill about in apparent random motion, but it will all become clear in the coming weeks. There is a purpose to everything you see. Some of this purpose you'll be told about, some you'll have to ask about and some will remain a mystery for the rest of your military career.
And if some bloke starts shouting at you, don't take it personally. You'll note that he shouts at other people as well. It's just his job.
Also, you may find you are told that the Unit does monthly recruit intakes, and after getting a brief to "come back at this time". Although this is the case in my unit the actuality is the brief is just done anyway and people are got in , so dont worry too much. You may have to take away a big envelope of paperwork to complete if you are happy to join the unit - have fun with that
Make sure you don't look a mess as already stated, you dont need a suit unless you want a commision (in which case it may be good to wear one), and you can get away with jeans and a shirt.
On the gate just say you are there thinking about joining (the prompt for this will be a soldier who will turn out to be the newboy staring at you with a confused look or blank look) and you will be pointed/taken somewhere.
You may not be the only recruit, which is always good, groups are safer if the RSM walks in
Make sure you have an idea what the unit is about, you should know or be able to find out their role (Air Corps, Infantry, Tankies, Engineers, Medics or whatever)... but dont find out too much or you'll get bored when they tell you it. Check to see if there are any other local units and check them all out.
The most imprtant things (that spring to mind) is to be yourself, make an effort to be sociable and employ a bit of self confidence without acting cocky. One of the major turn offs to your future colleagues will be if you try to show off, but you still have to show what you have to offer, so it is a balance, everybody has their own.
As for after the drill night, when the bar almost certainly to be opened, beer tokens, as mentioned, will be a must. Personally I wouldn't offer the first green guy I see a drink, but everyone's different. Use the opportunity to learn and show yourself as someone who is prepared to stay back and socialise.
Also take an extra layer of skin - not being from a military background I can see how somebody from civvy life could get easily offended by the wind ups, urine taking and sick humour, which is all in good faith! For instance, reference the comment about the chap wearing the crown on his uniform - when this guy comes over to take your tea/coffee order, he will probably spot that you are new, and try to pull a fast one when you give him your brew preferences. He will probably start screaming obscenities at you, and calling you lots of colourful names you'd never heard of before. Humour him and smile sweetly, for this is army humour