Where I live, this is what you do:
If you don't know where the stops are, you can go to the bus' website to find the routes and time tables. There's also a tool that tells you what bus to catch and when depending on where you start, stop and time. That's also where you find out what the fare will be.
When you know which bus to catch at which stop, you walk to the bus stop and try to be at least 5 minutes early. Have your cash ready - exact amount only, because they don't give change.
As the buses approach, look at the sign at the top of the bus - that's where the route number and name will be. It's usually a fairly basic description of the final destination, so if you're not sure, just ask the driver if the bus goes to your destination.
Deposit your fare in the collection box and find a spot to sit or stand. The front of the bus is usually set aside for the elderly or disabled, so if you sit there you need to be ready to move should and elderly or disabled person need a seat.
Pay attention to the streets as you pass them. Hopefully you have a general idea of where you're going since I find that landmarks are better indicators than street names. They're easier to see, too. As you get close to your destination, pull the rope/cord or press the button that's marked to let the driver know you need off at the next stop.
If you're sitting near the window and need to cross over someone to get out, politely excuse yourself and head to the rear door of the bus, if possible. Make sure you've got your things with you - umbrella, bags, etc.
At your stop, push the door if it doesn't open automatically. There are usually handles that are pressure sensitive, so push on those, not the door panels themselves. The doors are usually marked with something that says 'push handles to open' or something like that.
Step carefully off the bus and walk to your destination.