Rockets
A rocket works by turning the fuel into a hot gas. It does this by pumping the fuel into the combustion chamber, where it meets oxygen and ignites. The hot gas is then forced through the throat and out the nozzle. Most rocket engines use liquid fuel, fuel like liquid hydrogen or liquid methane. It's a liquid because as we all know, gas is a lot less dense than liquid, it is a way to add more fuel without having to worry much about pressure. Gimbaling works by moving the whole combustion chamber and nozzle with hydraulics. These engines can be turned on and off and can be throttled. However, they're very expensive and complex.
Other engines use solid fuel, they ignite near the top and burn. These types of engines can't be turned off or throttled once ignited. The good news is that they're very cheap and easy to make, as far as rocket science goes. The bad news is if these are damaged in any way, even a minor one, they will explode like fireworks. They're often called SRBs or solid rocket boosters, there are the tall white pillars you see on the sides of the space shuttle. You'll see tiny thrusters on the side of the SRBs, they're called separation motors, they ensure the SRBs won't hit the vehicle during separation.
History
Rockets were first invented by China in the year 1232. The rocket was a tube filled with gunpowder with a cone on one end and exposed on the other. When ignited, the powder burned producing smoke and flames that escaped out the open end creating trust. There was a stick shoved in the center of the gunpowder. The stick acted as a guide to keep it pointed to its target. This simple rocket was used as a defense system for the battle of Kai-Keng. Over time, people made bigger and better rockets but still were used for war.
In 1915, Robert Goddart experimented with solid-fueled rockets, the first rockets he built were small and had some form of solid fuel. One day, Gaddart became convinced that it was possible to make a liquid-fueled rocket. No one had ever made such a rocket before. He knew that there had to be a fuel and oxygen tank, turbine, and a combustion chamber; he designed and built many rockets, most of which failed. On March 16, 1926, he finally succeeded in building a liquid-fueled rocket. His rocket used gasoline and liquid oxygen and flew about 8 feet off the ground with a burn time of 2.5 seconds. The first of its kind. Nasa later named one of their science laboratories after him in his honor.
Orbit
Imagine throwing a ball straight up, the ball falls back down. Now imagine throwing it forward, its path is in an arch. If you throw that ball harder, it will have a bigger arch. That's basically what an orbit is. The gravity of the earth pulls objects down, but if you are going fast in one direction (not vertical) then the curve of the earth pulls away before objects crash into it. It's only possible in space. If you did this in the earth's atmosphere, the arrow-dynamic stresses will destroy it. When traveling close to the earth, you'll go much faster than if you are farther away. Because as a spacecraft gets closer to the earth, the gravitational pull will make it go faster.
When going into orbit, you'll need to do a gravity turn. I already mentioned how it works and why it's important. Once your apogee exits the atmosphere, then the engine will shut off and it will coast to its apogee. Then it will turn the engine back on to get into a circular orbit. If the engine didn't turn off, then it will have a highly elliptical orbit, not good. When raising an orbit, you'll want to start your burn at your perigee, accelerating to raise your apogee. Once your apogee is at an optimal height, you start your burn at your apogee accelerating to raise your perigee.
Reentry
There is no air in space, so there is nothing to push on. Plus, we are going insanely fast or 7 miles per second to be specific. There is only one way to slow down, by re-igniting the engines. You'll want to do this at your apogee decelerating, it wastes the least amount of fuel. Doing this lowers your perigee. It's a bad idea to slow down completely because it wastes a lot of fuel and you may reenter the atmosphere before you finish. Is also bad to slow down too little, the atmosphere won't slow you down in time and you'll go back up in space. But when you get it just right we re-enter in a reasonable amount of time and without wasting much fuel.
Just before we reenter the atmosphere, we'll need to heat shield first. If you don't, you'll burn up upon reentry. We are going at a speed of about 4 miles/second, and entering the atmosphere at that speed will create plasma. During this time, the heat shield will be experiencing a temperature of about 3,500 degrees Fahrenheit, which is hot enough to evaporate platinum or a third as hot as the surface of the sun. However, this is very misleading. Most heat shields are made from aluminum. The metal melts and then falls off bringing the heat with it, reducing the overall temperature. It doesn't have time to evaporate.
When we're going at a safe enough speed, we can deploy the parachutes. The drogue parachutes are deployed first to slow us down enough so we can safely deploy the main parachutes. If we were going too fast, then the parachute would rupture. There isn't a slow speed when doing this. If the main parachute did rupture, there's usually a backup parachute. The space shuttle did something different, it did have parachutes but would only use them after touchdown. Once it passed through reentry, it glided to the runway.
This is from a project I did a few years ago