There are lots of great tips in this thread, but it doesn't look like anyone has outlined all the steps you'll go through from start to finish for your trip. I figured I'd write that up, just in case it's helpful to you or anyone else who finds this thread later.

Lots of this is obvious, so please don't take offense if it sounds like common sense - I figure it's better to be thorough for future travelers' benefit

• Sign up for the airline's frequent flier program and add the number to your itinerary on their web site. Doing this in advance can actually make your life easier at the airport - if you ever need to ask an airline employee to look up your flight information, knowing your frequent flier number can make that easier on them.
  
  
• Figure out how you're getting to the airport. Everyone has their favorite way of getting to the airport, and this varies from city to city. I prefer public transportation whenever it's available, but here in Seattle our light rail doesn't serve the neighborhoods I live in and the bus service is a bit spotty. (If you go this route, pay attention to make sure your flight times match the schedule, and allow lots of extra time.)
  
  If you choose to drive, carefully consider where you're going to park. If flying out of a small airport, like, say, Roanoke, VA, this is easy - just park at the airport, as the cost should be very affordable. If you're flying out of a big airport, though, onsite parking can be very expensive (again in Seattle, it's $30/day or something obscene like that). If so, you can bet there will be lots of reliable offsite parking lots like MasterPark, The Parking Spot, etc. that cost a fraction of that per day. Either way, you'll likely take a shuttle bus from the parking lot to the checkin counter, so allow time for that.
  
  A cab or a shared van service is also an option - ask around to find out if this is an affordable choice in your area.
  
  Finally, you can always bum a ride from friends. That's a good idea, too. (Which reminds me, I need to call in a favor to get a ride for my own next trip! )
  
  
• Arrive at the airport about 2 hours in advance. If it's your first time, you've got plenty of time, and you're nervous or curious, it won't hurt at all to get there 3 hours in advance. Once you get through security, if you have extra time you can just explore the terminal - one of my favorite pasttimes.
  
  
• Proceed to the airline's ticket counter. I recommend heading directly there as soon as you arrive at the airport.
  
  You may notice skycaps (baggage porters) at the curb who offer to help with your luggage - I usually politely decline or avoid them, since they work for tips and don't offer any services that the airline itself doesn't.
  
  
• Use the airline's kiosk to check yourself in. If you're checking bags, indicate that on the kiosk and pay the checked baggage fee; if you're not, just collect your boarding passes.
  
  This is one step you can experience at home - Delta has a really cool demo of their checkin kiosks at http://www.delta.com/traveling_check...demo/index.jsp that will walk you through the whole process. Continental's kiosks work almost identically, so this should be applicable for you.
  
  
• Or not. As an alternative to the kiosk, you can check in on the airline's web site from home. Just print your boarding pass and skip the kiosk entirely. Less of the airport experience, but you do save a few minutes
  
  If you're checking bags, you can still check in at home first and pay your bag fee online. Many airlines offer a discount of a few dollars if you pay before you get to the airport, in fact. If you do this, you still check your bags at the ticket counter kiosk - just log into the kiosk by scanning the boarding pass barcode you printed at home.
  
  
• Clear security. Again, I recommend doing this immediately after you've checked in at the ticket counter.
  
  Much has been written about this elsewhere, so I'll just add one tip: due to a variety of concerns (take your pick of radiation or privacy), I urge you to use your right to opt out if selected for a backscatter or millimeter wave scanner. (They're different than a metal detector - typically much larger and curvy with a video screen on the side, while metal detectors are thinner and boxy. You only need to speak up to say you opt out if they wave you towards that machine - if you're directed into a metal detector instead, you weren't selected for screening.)
  
  If you opt out, you'll get a brief patdown from the TSA - not nearly as invasive as you may have heard in the media, and in my opinion preferable to the alternative.
  
  
• Check monitors to find your gate assignment. This is the first thing I do after clearing security - flights often change gates at the last minute; just like in a parking lot, sometimes a parking space is taken when your inbound aircraft arrives
  
  
• Proceed to your gate. If you got to the airport early, this is a great opportunity to explore - check out the shops, grab a bite to eat, whatever you like!
  
  Whatever you do, be at the gate no later than 35 minutes before scheduled departure. The departure time on your ticket is actually the time the airplane pushes back from the gate and the door closes - to make that time, they'll close the gate 15 minutes before departure, and if you're not there by then you'll miss your flight.
  
  
• Follow the gate agent's directions to board. Usually this is as easy as listening for the zone number printed on your boarding pass and boarding when it's called.
  
  
• Have a great flight!
  
  
• When you get to your connecting airport, your first move should be to look for the information monitors again. Often, they'll even post connecting flight information right at your inbound gate - if so, you're in luck, but if not there should be monitors only a few steps away with flight listings.
  
  Find your gate number and follow the signs to get there. How rushed you are just depends on how long your layover is, but in almost all airports 45 minutes is enough time, and anything over an hour should give you plenty of breathing room.
  
  
• If something goes wrong or you miss your connection because your inbound flight was late, don't panic! Just find any airline employee and they'll be happy to point you in the right direction and get things fixed up for you.
  
  
• In the highly unlikely event you get stuck in a really bad situation, like severe weather or a cancelled flight - I recommend calling the airline while you wait in line to talk to a ticketing agent. You might get through faster and score a better route to your destination by being proactive. (This happens to me about once a year, and I fly 60+ segments - it's really not as common as you might think.)
  
  
• Board your second flight! Same as before...
  
  
• Arrive at your destination. Once you arrive, follow signs to "baggage claim and ground transportation". You'll walk past a TSA guard preventing people from walking in the exit, and you're done!
  
  
• If you checked bags, you'll reclaim them at a baggage carousel. There are usually signs assigning a carousel to a particular airline or flight, but in some small airports there may be only one or two carousels shared by everyone.

Hope this helps! If you have any more questions about the process, I'll be happy to revisit this post and fill in the gaps for you - just ask!

Enjoy your flight