Of course they check tickets... they don't want someone who bought a short flight to get on a plane for the other side of the US!
As for finding your way around an airport they really are pretty easy. You will
1) Arrive at the airport and follow nearby signs to park. Depending on the size of your airport you then either walk or take a shuttle to the ticketing area.
2) From the ticketing area there will be sections for each airline you will find yours and bring your bags there. If you didn't print your boarding passes at home you will do this here as well as checking your bags.
3) Go to security - Your from canada so I can't help with what that is like. Hopefully someone else can but I assume the US is different.
4) Optionally if you have alot of time go get some food or shop
5) Find a monitor and find out what gate your plane leaves from. They may have told you when you checked your bags but I always double check now because they change them sometimes
6) Follow the signs to your gate (generally they have "wings" with letters and then the numbers just go in order so its hard to get lost)
7) Wait at the gate until its time to board. I don't know how your airline does this but every airline I have ever flown explains it.
Continuing on...
8) Once onboard, find your seat, put any carryons under the seat in front of you or in the closest overhead bin
9) Sit down, buckle the seat belt.
10) Relax & enjoy the flight. As mentioned, electronics will need to be turned off during the departure and arrival (they'll tell you when), so plan accordingly. The engines will be loudly humming and there will be lots of noises during arrival and departure (landing gear up/down, flaps & slats up/down).
11) Once you arrive at the next airport, when the plane gets to the gate, unbuckle. Depending on where you are in the plane will determine how much room you have. Once you have room, gather all your belongings and exit the plane. Don't stand in the aisle getting your bags organized. Someone behind you might have a tight connection. If you need to organize something, step out of the aisle.
12) When you walk off the jetway, look at the monitors or ask an employee where your next flight is. They'll want to know your destination. Find that gate, stopping for bathroom/food on the way (if time). Follow steps 5-12 for your connecting flight.
13) At your final destination, once you get off the plane, look for signs that say "baggage claim" (if you've checked bags, this is where you'd pick them up (unless you used DME), or "transportation/exit" if you don't need to get bags. If you're using DME, go to side B, level 1.