There is so much information and so much to understand about hydrogen, most people get stuck just trying to understand how you put it in the gas tank. (joking, but seriously) Do your research on the different type’s hydrogen fuel cells, but basically the most common both used compressed hydrogen. One converts the hydrogen gas to electricity and the other burns the hydrogen in the combustion chamber.
Now the 3rd most popular type is Hydrogen On Demand, or Hydrogen Assist, or Hydrogen-Hybrid. It's called many different things, but the basic principle is that it's an add-on to your existing gasoline engine and it makes very small amounts of hydrogen and oxygen. The engines intake sucks in they mixed gas and the "theory" is that it enhances the engine's efficiency.
You'll find all over the internet that this technology doesn't work as it goes against the laws of conservation of energy, so on and so forth. On paper it doesn't make sense and it's a crazy concept to grasp, but some people have tried it and succeeded while most have failed.
Here's the reason most people have failed: Due to the emissions laws and regulations be coming strict, more and more emissions sensors are added to vehicles every year. The vehicles (most) computers are designed to burn at 14:1 fuel ratio (14 parts air to 1 part fuel) and they correct and adjust as needed.
When you add a hydrogen cell to a vehicle the vehicle's O2 sensors sense the change and dump in more fuel to compensate to get you right back to 14:1 as it's designed.
Most people don't realize this, but the gasoline engine is only about 15-30% efficient. So you put your fuel in, the engine burns it (well sort of) un-burned fuel hangs out in the catalytic converter until it's burned, some vehicles recirculate the fuel partially, and then it escapes your tail pipe with very little pollutants. Most of the energy escapes in the form of heat and does not get used. So the theory goes, if you are able to increase the efficiency just a tiny bit it will add up to money saved.
Good news/Bad news: There are ways to get around or trick your vehicles computer; unfortunately it's not simple as downloading an app. You can get a chip for your vehicle to help compensate for this such as a Volo HHO Edition, however your results may vary at best. On the more advanced side (in some states illegal) you start messing with the emissions sensors to lean out your fuel mixture, typically with a correct install, correct amp draw and the right gas production for your vehicle you'll drop approximately 20% of your exhaust temperature. Cooler exhaust temps allow you to lean our your fuel so instead of being stuck at 14:1 you can add more air to your fuel mix and use less fuel!
If this sounds like a lot of work, then go buy a Prius or other "Green" Earth saving vehicle. (If you can justify the cost, I haven’t yet aside from the “cool factor”) If you are willing to spend time, frustration and tears to try and make this work then it may be for you.
The Internet is full of overpriced-waste your money kits, I haven’t found a site that sells a kit that’s really worth investing in yet. I pieced together my setup from different sources on the internet and the hardware store and didn't really save a whole lot “piecemealing”. It was an extreme hassle to get everything work and agonizing, but it’s fun to experiment and watch it working. There’s nothing free with this, you either spend your time figuring it out or pay someone to do it and you still may not be happy with the savings or results and keep in mind that some vehicles work better with this than others.
I’d suggest for anyone starting out to keep your setup simple, so maybe start with a wet cell design and do your homework! There are many people that sell instructions on how get an HHO cell working on a vehicle, it may be worth investing in one of these books, or e-books if you don’t feel like spending hours dissecting the internet for bits and pieces like me.