Yes, but it requires some constants that I don't have on me right now (you can find them in the Handbook of Chemistry and Physics, if you can get your hands on that. You can also probably find them online if you know where to look).

Step 1.
Hydrogen and oxygen combine to make water and release energy. I don't know how much energy this is; this is the first thing you will need to look up. The ratio is2 moles hydrogen (2 grams) to one mole (16 grams) oxygen will make one mole (18 grams) of water vapor.

You will be adding hydrogen and oxygen together at a certain rate, which is determined by the design of the rocket. So, you can pick whatever rate you want based on how fast you want your rocket to burn through its fuel.

DON'T assume that you can get oxygen from the air!Oxygen is in the air, but for a rocket engine you will need it faster than you can get it in the air.

Step 2.
The water vapor created by burning the two gasses will be very hot, and will exert a pressure on its surroundings, including the engines of the rocket. The amount of pressure that it exerts will depend on the temperature. Use the following formula:

Tnew is the temperature of your water vapor Told is the temperature of the oxygen and hydrogen before you burn it (this will be cold, probably) E is the energy released from the burning (what you just looked up in step 1) k is the heat capacity of water VAPOR (NOT liquid water!). You need to look this up also.

Step 3.
This pressure is what will provide the rocket's thrust. You can calculate the pressure with the following formula:

T = temperature (in Kelvin) that you just calculated.

Step 4.
Pressure is force per unit area, so what you need nowis the area of your engine where you are burning your fuel and expelling the gas. You want only the area of the roof of the burning chamber, however, so this usually means the area of the exhaust ports on the underside of your rocket.

Note: expelling the gas will empty the chamber, so you will need to add more fuel. As a result, what you probably want is the amount of impulse, which is force over time that you are generating by expelling the gas. PV = (2/3)NKE is a good equation to use, N is the number of atoms and KE the kinetic energy you are getting.

Step 5.
You now want the acceleration generated by your engine, which depends on the mass of your rocket:

F = ma

This is how rapidly your rocket will move. Remember, if you are trying to launch your rocket up, you will have to counteract gravity. The acceleration due to gravity is 9.81 m/s², so in order to get anywhere, you need more than that. The Space Shuttle, I think,has a total acceleration of about 13 m/s², which means that it is accelerating at 3 m/s² relative to the Earth as it leaves the launch pad, because of gravity.

Yes absolutely. There are many good books on this subject. It requires college level chemistry and calculus but if you are motivated, you can learn that stuff pretty easily as once you wrap your head around the basic ideas, then it comes rather easily.

Without getting into too much complexity, the basic idea is that a fuel liquid hydrogen and an oxidizer liquid oxygen are brought together and allowed to react in the engine. This reaction produces water and liberates a lot of energy (enthalpy, actually). This enthalpy raises the temperature of the reactants and a product to VERY HIGH temperatures on the order of 2000-5000K... gas at such a temperature has a lot of kinetic energy.The speed of the exhaust is ROUGHLY found by

deltaH=1/2V².

Where delta H is the enthalpy change of the combustion reaction per kg and V is in meters/second.

A place to start learning about this is a book called explosive shocks in air by Kinney and Graham.

Books on rockets are in UCSB library.If you want to know more you can write to me directly.

One thing you can get into is model rocketry. These rockets use solid propellants and are less energy rich than liquids but they are something you can do as a kid. Fooling around with liquid hydrogen is not something you want to be doing.