Hi dowensrf13,
Welcome to the HVAC Group!
If you write down these few tips it will make replacing relays much easier. Always go by the manufacturer schematics when available. You will usually run into two types of relays, the current and potential relays. The Potential has its terminals 1,2,and 5. 2 and 1 are the normally closed set of contacts connected between the start winding and the start capacitor to open and take the start capacitor out of the circuit. Therefore, 1 is always connected to the start capacitor and 2 is the wire from the start terminal on the compressor. 5 is our wire from our common on the compressor because it is connected to the coil and provides voltage.
On your current relay you have your terminals L,S, and M The S from the relay always goes to one side of the start capacitor and the other terminal on the capacitor goes to the S on the compressor. The L on the relay always goes to Line or power. The R on the relay goes through a built in coil and to R on the compressor. The C on the compressor would go to the other Line or power. Of course we would have switches and/or thermostats included.
With some practice you will get to know how to wire these without even looking at a wire diagram.
Relays have a set of contacts together with a magnetic coil mechanism which controls the contact position. The contacts may be normally open or normally closed when not energized, and a given relay may control more than one set of contacts. When the coil is energized, the contacts reverse their action and make or break circuits as desired.
Most relays are of the potential type, and are actuated when the coil is energized with the proper voltage.
Current relays are actuated by a sufficient current flowing through the relay coil, and are normally used when it is desirable to make or break a circuit when a large change in current flow occurs. These are used in single phase motor starting circuits, and occasionally in safety circuits.
Good luck with your studies!