It's really pretty easy.
With most airlines, you can check in for your flight the night before, through the airline website. Then when you get to the airport, all you have to do is check your bags. If this is not an option, then go to the counter at the entrance to the airport (or some airlines have machines that you use to check in, kind of like an ATM). The machines are self explanatory. If you use one of these to check in, they will come and collect your bag from you, if you have any bags to check. After you are checked in and your bags have been collected, then you will proceed to security. When you go through security you will have to remove your shoes, take out your laptop (if you have one) as well as your bag of liquids (if you have one.) All of your liquids must be in containers marked 3oz. or less, and all in 1 quart size baggie. Items such as deodorant and chapstick, also need to be placed in along with any shampoo, conditioner, toothpaste, etc. Once you get through security, proceed to your gate. When it's time, they will start boarding the plane. Airlines board differently, but generally you will have a seating group printed on your boarding pass. When they call your group number, board the plane. Once you reach your final destination, follow signs to the Baggage Claim, if you have bags you need to collect. Have a great trip!