Carry a toolkit and spares! Your toolkit should allow you to remove both wheels and other stuff you may need to do to get you home (access spark plug, replace levers, etc). When you do work on your dirt bike, use the tools you carry with you so you know that you've got the right selection when you're out and about. Obviously you only need to carry a reasonable toolkit, no need to stock up like a Snap-on van
Tyre levers, takes these if you're running tubes and always carry at least one spare tube (a front will fit in the rear as a get-you-home fix). Carry a split link for your chain and a way to fit it if you need to. If you run mouses or TuBliss you won't need to carry tubes, but their legality is questionable at best (plenty of debate about that!).
Join the TRF, contact your local group and find out where the legal lanes are. Don't ride like a twat thinking you're an enduro god as 1. You'll hurt yourself and/or someone else (unless you are an enduro god, there are plenty about on here
), but more importantly 2. You will upset people which can lead to conflict and ultimately lane closures.
Look after your chain - after washing my bike and riding it to blow some of the water away, I used to coat my chain in clean, cheap, engine oil. It prevents rust when the bike's out of use, lubricates it, although obviously flings off when you ride. Some people use chainsaw oil which flings less. Don't use lube from your roadbike - it will attract dirt and turn into a grinding paste and your chain wont last long.
Carry a mobile for emergency use. Try and ride with others, having a fall/getting stuck when alone can be a painful and depressing experience.
Do invest in some proper off-road kit, perhaps after a few outings and you've decided you like green-laning. As has been said, road stuff will suffice for gentle green-laning but won't offer the protection of dedicated kit in a hard fall, especially boots. Oh, and you'll look like a tit
Most importantly have fun and let us know how you get on.