(B) at most big airports, in fact, you can "check-in" -- so, leave your luggage with them - right on the road where you get out of the taxi. sometimesSometimes you do that and you ALSO have to then checkincheck-in at the main checkincheck-in counters inside; sometimes all the checkincheck-in is handled at the roadside.
(B2) To add more confusion, these days you can often check in using a machine that looks like an ATM. Instead of having to line up to talk to a human at the check-in counters, you line up to use a little sort of machine; they might have a row of ten or so of these machines. You just type in your numbers and it prints out the boarding pass for you (see image above). Note that in this case you have to put your bags "somewhere", sometimes a person comes and gets it, sometimes you use the roadside system, sometimes you then go to another counter etc. Personally if it was my first time I'd just go to a human at a checkincheck-in counter! I would not use the "automatic machine" nor the "roadside checkin"check-in".
(B3 !!) And note that these days, you sometimes do not need to check-in at all! If you strictly have only hand baggage, in some cases you can "check in online." You do that at home before even before going to the aorportairport. I would avoid this if you are new!
(C) note that check-in is the part where you "have to wait" - those are the long lines you see at airports. it can often happen you have to wait for an hour in the line. some people like to arrive very early, to be the first to check in, so you don't have to wait. note that by doing that you can get a better seat (BUT that does not apply so much these days, as explained above,: you can usually getchoose your seat in advance, online.)
the wait to go through security CAN BE very long, particularly say in the US. often there is no wait at security. the wait to actually board is no big deal, you all just line up and go on the plane.