Solid fuel (solid propellant) rockets use pre-combustion fuels that at air temperature exist in non-liquid, non-gaseous form. Solid fuels are comprised of fuel energy component(s) and oxygen-providing, fuel combusting component(s).
Once the exothermic (heat-releasing) chemical reactions between fuel and oxidizer are begun they cannot be stopped. Thrust is acheived by the conversion of solid propellant chemicals into gases that exert forward pressure on the wall of the combustion chamber opposite the exhaust nozzle through which the gas pressure within the chamber is vented.
In the case (hey, a pun) of a shuttle solid rocket booster, the solid propellant is 69.83% ammonium perchlorate (oxygen source), 16% powdered aluminum (fuel energy source), 12% polybutadiene acrylic acid acrylonitrile polymer (rubber, makes the fuel the consistency of an eraser when cured), 2% curing agent, and 0.17% iron oxide catalyst.
You'll see the numbers in a Google search, too.
