Before you set off check that you have everything you need. Your organiser is likely to have sent some documentation, but the minimum generally required is:

A Van - Hiring a Transit is the way to go. It's cheap, and saves you worrying about riding there in the rain, it allows you to load up with all the stuff below and take your partner in comfort. At the end of the day you'll probably be whacked out, and it's less stress to drive a van home than ride. On top of that you don't have to worry about how your getting home if you bin it . . .

Driving Licence - Most circuits require a valid driving licence.
Boots.
Leathers (1 or zip together 2 piece).
Gloves.
Helmet. In addition this stuff will be useful:
Petrol - Sometimes unavailable at circuit and expensive when it is. You'll use more than you think. Also 2 stroke oil if you run a 'stroker
Gaffer tape for lights / mirrors / indicators & minor repairs.
Soft Drinks & Chocolate - It's easy to get dehydrated, and you'll be working much harder then road riding.

Driving Licence - Most circuits require a valid driving licence.
Helmet.
Race suit - probably optional but check with your organiser. In addition this stuff will be useful:
Gaffer tape for lights / mirrors / indicators & minor repairs.
Soft Drinks & Chocolate - It's easy to get dehydrated, and you'll be working much harder then road riding.
Tidy up the loose stuff that might be floating around your car.
Coolant, either be it deionised water or antifreeze.
Just before you get to the circuit full up with fuel. Fuel is sometimes unavailable at circuit, and expensive when it is. You'll use more than you think.

Signing on. A sign will direct you to the organiser's office where you'll sign on. Signing on consists of showing your licence, and being issued with a numbered sticker to put on your car or /bike. If you've not already, you'll choose your group (slow, medium, fast etc.) and pay the photo man if you want photo's.

Driver/ Rider briefing. Prior to being allowed out on circuit, organisers ask that you attend a briefing. This will cover how the day will be run, do's and don'ts, flags and safety information. Even if you've been to a track day before, always attend the briefing. You never know if something out of the ordinary is on for that day.

Scrutineering / Noise test. While I've never been subject to actual scrutineering or even had my gear checked, I believe that some organisers do check vehicles prior to allowing them out on track. All circuits have noise limits, some test before they allow you out on circuit, while others have a noise meter next to the pit wall. Your organiser will have a noise limit that they are not to exceed. If you do, you'll be stopped from going out next time. You're only likely to have problems if you have a non standard exhaust system. Some organisers expect bikes or cars to be road legal, though I've never seen this enforced.

Track Time. Most days split their riders / driver into groups, graded by ability. Most days have 3 or 4 groups, running 20 minute or 15 minute track sessions. Some organisers run mixed car and bike days. Don't worry, bikes will be in one group, cars in another. Lunch is normally for an hour to give the marshal's a break. People say that the session after lunch is the worst for "off's". People eat too much at lunch and go back out on track a bit too relaxed. Some riders & drivers forgo the final session. This is partly superstition, and partly not wanting to push their luck.

The first session is often lead out by an instructor, to show the way around, and get engines and tyres warm. Take your time and don't be in too much of a hurry. You may find it will initially take half a day before you are confident you know your way around the circuit. Don't get drawn into racing some one faster than you before you know where you're going.

These are my tips for better track day riding - I'm no racer or expert, though I've been riding for 15 years and doing track days for 3. These are the things that have helped me.

Top Tip #1 - It's easy to be drawn into 'turning in' too early. You'll apex sooner than ideal, and worst case run out of circuit on the exit. Try and turn in & apex later.

Top Tip #2 - Try and pick out breaking and apex points on circuit. The turn in and apex may already be coned. By looking at the point you want to apex at you'll magically get closer to it.

Top Tip #3 - In the rain, you may find more grip off the usual racing line.

Top Tip #4 - Remember to smile.

These are just general things that have helped me. Don't be afraid to ask an instructor for advice if you need it.