Gear you will need

Every time I have visited the cave, I have seen people who did not come prepared. Unfortunately, if you don't have the right gear, it's nearly impossible to explore the cave, and it is certainly not enjoyable.  The equipment you need for the cave you probably already have- 

Absolute Essentials

3 Sources of Light

Warm Clothing

Sturdy Shoes

The light sources can be anything from a propane lantern to an AA cell flashlight- just make sure you have back ups- and extra fuel or batteries. Standard 6 volt lanterns work really well. 

Bring a sweatshirt and sweatpants- and some sturdy shoes. The shoes are more essential in the upper cave, but even in the lower cave you should have at least some hefty sneakers. Standard running shoes are adequate for the lower cave, but some of the lava formations are sharp enough to shred the material on them. Open-toed sandals and thongs are definitely not a good idea- (even though I have seen people attempt it... wasn't a pretty sight.) 

Not essential, but nice to have:

A headlamp, so your hands are free
A hard hat or a bicycle helmet
Kneepads (I *will* have them next time...)
Disposable Camera with Flash