A roller coaster is usually made up of 4-5 different processes.
The Launch/Crest
Ride Dynamics
Block Sections
Final brake & Return
Some coasters (especially more old-fashioned) will have a different first step, called the ascent. This is where a chain or other mechanism hauls the train up a steep incline, in order to reach the height necessary for the crest. In newer coasters there are newer mechanisms that make this step optional, in which case the first step would be an immediate launch.
Now there are a lot of different roller coasters, and rides in general, so in order to keep things relatively simple, the main processes a coaster has to keep in mind is:
The mechanical system for the trains/track
The launch/acceleration system
The brake system
The mechanical system for a coaster is how it is designed and built. Some coasters have wooden tracks with steel beams, while others have tubular rails. Knowing the mechanical systems behind a coaster is crucial for its design. Design also varies per coaster. There are inverted or suspended coasters (the track is above the train), water rides/coasters (track is submerged/chain operated), and some rides are built for speed, while others for their unique loops or turns.
As an example, think about Lagoon. Some rides like Cannibal and Wicked have stouter trains, with more extreme drops and turns. Other rides like Spider have less extreme turns, but a mechanism that spins the train.
The launch or acceleration system for coasters also varies widely. Many newer coasters use electromagnet acceleration, which is much smoother, and doesn't rely on an ascent like older coasters. Other forms and systems that can be in place are chain, pneumatic (air pressure), hydraulic (oil/gas pressure), and lesser used systems like flywheels, catapults, and friction wheels. The system behind a coaster is often determined by the intended use for a ride. For younger audiences, a mix of chain lifts and hydraulics are common, while for older and more risk-taking demographics, electromagnet and hydraulics are becoming more popular. Pneumatics are interesting because they are often used in tandem with another system, like hydraulic or electromagnet in order to offer an enhancement of the experience, like smoother braking.
An example of this combination of acceleration systems is the Dwarf Mine Train in Disney Florida. This ride uses chain lifts for the main track, but a pneumatic system for movement within the train, or the rocking of individual carts throughout the coaster.
The final process is the braking/management process. There are two main brake systems used in coasters: Block brakes and trim brakes.
Block brakes are on every single coaster, and are required at the end of a ride to allow riders a safe exit.
Trim brakes are more cosmetic. They are used to slow a train in the ride, either to build suspense, prepare for a drop, or in case a train is moving too quickly. They can also be used as an emergency stop.
These brakes are programmed to understand where and when they need to brake. For example, trim brakes are used to "trim" the speed on a train to keep it at a safe level. They are used frequently, especially in coasters where many drops and accelerations are gravity based, and thus fluctuate slightly by car. Block brakes are programmed to completely stop the train within certain circumstances, most commonly at the end of a ride.
Now there are management systems for these brakes that help to keep the ride moving. One important aspect of this is block zones, which we'll cover in detail a little bit later in Safety and Thrills.
Some management systems for monitoring trains include RFID (used for monitoring riders and restraints specifically), Allen-Bradley (common system for brakes), and other PLC systems.