No matter where you are, systems break down to common components. Details do vary by climate and code but the basics remain. The sizes and quantities of each depend on the system. I'll list the basics first and some of the exceptions at the end.

Materials:

Starting at the end and working back, you will need something to spray the water, usually popup sprayers with nozzles, shrub sticks with nozzle adapters and nozzles, or rotors.

To connect these to the underground pipe you need either a cut off nipple or a swing joint. Swing joints are the most versatile and can help prevent damage over time. Risers will connect directly to the pipe with a Tee.

You will need PVC pipe and fittings.  The main runs need to be Schedule 40. The laterals, or zone lines, can usually be Class 200.  Local codes may have restrictions so check first. Fittings are the straight connectors, elbows (90 and 45 degree), reducers, couplers, Tee's for risers and generally anything that connects the PVC to PVC, including connecting to valves.

Speaking of valves, you will need some.  Each valve controls an individual zone. They turn the water on and off for that area. They go in valve boxes.

Before the valves in the water line you have a backflow preventer. This keeps contaminates out of the drinking water. Be sure to check your local codes for requirements. EVEN IF YOUR AREA DOES NOT REQUIRE A BACKFLOW, put one in. It's for your protection. Insulation for the backflow in most areas of the country. Also pipe insulation.

Finally, above the backflow in the water line you have two optional parts. An isolation valve, usually a ball valve, to turn water off to the system in case of breaks and leaks. It's not required but someday you will want one. Put it in. You may want a master valve. This is a standard valve used in a special manner.

You notice I have not mentioned copper pipe and solder. If your code requires you use this, and you are not very experienced in their use, get a professional. It can be difficult and painful.

Last in the line is the brain. Something has to tell the system when to come on and what to do. This is the controller. There are many types and models with varying features. If there is any chance your landscaping will change over the next few years, get one that is expandable. Modular is best.

You will need lots of wire, usually in red for power, and white for common. Multistrand is also available. Wire connects the controller to the valves. It's the nerve path from the brain.