Since you can't make Hydrogen quickly enough to power a car in real time, you must produce it separately, and store it as you store your Gasoline fuel supply in your vehicle now.
There are but 3 ways to do this:

1. Store the Hydrogen as a compressed gas.
2. Store the Hydrogen as a liquid.
3. Store the Hydrogen chemically bonded to a chemical.

We'll cover each option in order.

1. If you choose to store the Hydrogen as a compressed gas, you'll need HUGE tanks, and many of them, since Hydrogen isn't very dense, so a tank really can't hold all that much. In addition, you'll be driving a giant bomb. In a collision, expect to die in a huge fireball/explosion.

2. Choosing liquid does solve the density problem since liquids are far more dense than gasses, so you can reduce the amount of tanks and their sizes required to power the car. The new problem that pops up is the fact the liquid Hydrogen in cryogenic... in short REALLY cold. It requires vacuum-thermos ( dewar ) tanks and vents to exhaust the boiling Hydrogen gas. You'll also have to find a source for liquid Hydrogen which is far more expensive than Gasoline. You've also now increased you danger factor when it comes to a collision. Not only will you have more Hydrogen gas spewing around that's going to explode and burn, but you'll also have a liquid spraying about that's over 400 degrees below zero. Once you add in the added complexity of the system due to the cryogenic liquid, your vehicle will wind up being a giant, low efficiency, rolling bomb that costs more than your house, and costs far more to run than it did on Gasoline.

3. The 3rd option is simply the only way to go. There are materials call Hydrides that absorb Hydrogen like a sponge absorbs water. Typically, the tanks are filled with granulated Hydrides, and Hydrogen is pressurized into the material. Hydrides have many advantages over liquid & gas. One is that the density of the Hydrogen stored in the Hydride can be GREATER than that of liquid Hydrogen. This translates directly into smaller and fewer storage tanks.
Once the Hydride is "charged" with Hydrogen, the Hydrogen becomes chemically bonded to the chemical. Even opening the tank, or cutting it in half will not release the Hydrogen gas. In addition, you could even fire incendiary bullets through the tank and the Hydride would only smolder like a cigarette. It is in fact, a safer storage system than your Gasoline tank is.
Then how do you get the Hydrogen back out? To release the Hydrogen gas from the Hydride, it simply needs to be heated. This is either done electrically, using the waste exhaust heat, or using the waste radiator coolant heat.

For this reason, Hydrogen conversions are not recommended for vehicles with turbochargers, superchargers, or compression ratios greater than 9.5 to 1.
Also, because of the higher compression, different ignition system, and host of other factors,
the Hydrogen Fuel System will not work on diesel engines.