Just to repeat Relaxed's excellent answer. Yash, the process is:
(1) PURCHASE a ticket. These days, that is almost always online at say Expedia, or over the phone. You'll get some sort of purchase code, like XFD123HHC
Note that these days, it's usually confusing since there is both an EXPEDIA code AND a code from the AIRLINE! (Possibly even more than one airline.) So, write all those down, or if you prefer print it out from your computer.
(2) CHECK-IN. At the airport, you "check-in". This means you give them your code numbers, and you show them your passport, and you give them your luggage. In return they give you your boarding pass.
Note, as it says you give them your luggage. But any small "carry-on" items, you just keep in your hand.
So, "check-in" is all about getting your boarding pass.
Boarding passes almost always look like this:
(3) Next, AFTER checking in, you go through security. You have to show them your boarding pass and also your passport again. They scan you and your small "carry on" items. You then enter the departure area of the airport. Only people who are actually flying, can go there - you have to say goodbye to your family as you enter the security check point.
Now - you go shopping! :) There are always shops in the departure area. In any large airport, it is like a shopping mall. Once again, the only people in the departure area are people who are actually flying - they have a boarding pass in their hand. (And of course people like police, shop-keepers etc who have special passes to be in the "passengers only" area.)
(4) Finally you board the airplane. This happens at the gate. You have to give them your boarding pass and show them your passport. At the gate they remove and keep the large part of the boarding pass (on the left in the image above) and you keep the small part (on the right). The only reason you keep the small part is to remember your seat number. (if you happen to drop it or lose it it is no big deal.
So after shopping, you all stand around at the gate. Eventually they will say "Now boarding, your flight 247". You all line up and go through the gate - as I explain, they take your boarding pass, you show your passport, and they give you the small tear-off piece. At that instant you do and must walk straight on to the plane (down the walkway) and that's you on the plane. (You cannot go back to the shops, or anywhere else, after that.)
To recap:
(1) purchase online. Give: credit card number, Get: reservation number(s).
(2) at the airport: check-in. Give: reservation number(s) + luggage. Show: passport. Get: boarding pass.
(3) at security. Show: boarding pass + passport. Get scanned (you and your carry-on bags).
You're now in the "departure area" which is often like a mall. Passengers only.
Wait until you hear "Flight 247 now boarding at gate 44B..."
(4) at the gate. Show: boarding pass + passport. Walk on to the plane and sit down, you cannot return to the departure shopping now.
Notes:
(A) traditionally, you only got your seat assignment at the moment of checkin. ie on the actual day, at the airport. However these days...on the web, after you buy the ticket, typically you can click and actually choose your seat, so that's good. (In fact, nowadays, most airlines now have a con where you can then pay a little more for a "better" seat.)
(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. sometimes you do that and you ALSO have to then checkin at the main checkin counters inside; sometimes all the checkin 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 checkin counter! I would not use the "automatic machine" nor the "roadside checkin".
(B3 !!) {Finally today you sometimes do not need to check in at all - ie, if you strictly have only hand baggage. You can "check in online" at home. 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 get your seat in advance.)
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.
I hope it helps you, or some other readers! more and more people are flying for the first time, so, enjoy.