New flyer: What do I do with my luggage?

Yes, this seems like a very silly question, but I'm trying to prepare in advance. I'm flying at the end of December and don't exactly know what I'm doing. I've only flown previously 1 time and that was with a school group, so I just kinda followed what everyone else was doing.

So, here s my question: I plan on bringing both a carry-on and luggage, but what do I do with my luggage? When I flew previously, we took all of our stuff to our gate and when we were about to board the plane, someone took them to put under the plane and when we reached our destination, our luggage was waiting for us when we got off, but is that standard for all airlines? I get kind of confused when people talk about checked luggage and baggage claim, so I figured I d ask.

Do you only check your luggage in at check-in if you have multiple bags? Is that where baggage claim comes in?

TIA.

Added (1). I don't know if this matters or not, but when I traveled with school, I flew from BNA to LGA with Delta. This time, I'll be flying from BNA to YYZ with WestJet.

How to book cheap flight?

I'm trying to book a flight from the Heathrow (UK) airport to Orlando (MCO) international airport. I'm using expedia.co.uk for a flight and it is showing the departure flight as 300 pounds and the return flight as 0 pounds. Why is the return flight 0 pounds? Other sites show the flights costing 600 pounds or more. Is there some sort of catch?