Great news...I am finally back from travels, got some time to spend this weekend with my ArduCopter and got it airborne yesterday! :) Thanks to the help y'all provided here, plus a little additional online research. In a nutshell, below are the things that got the copter going for me (just in case there are any other noobs out there who need additional 'getting started' help). There is, of course, a lot of great online material for getting the ArduCopter up and going, but for some reason, not everything seemed to logically flow for me (being a noob)...I think some of it just makes assumptions about the people who buy these copters. I'm not providing extensive detail here, just the key steps. If any others want details on this to help them, let me know and I'll send or post it. Anyway, the key things that got mine going were:
1. Download the Mission Planner software, connect the copter with the USB micro cable, and install the latest APM firmware
2. Calibrate the ESCs (as was pointed out by Ted). This was a bit tricky and I think I didn't do it exactly right the first couple of times.
3. Now you should be ready to arm the ESCs (still without propellers!). On my Spektrum DX8, this is done by holding the throttle all the way down and to the right for about 3-4 seconds, after which time the red LED on the copter will switch from flashing to solid. However, as discussed in #5, I somehow had some of the levers reversed, so that it actually required me to hold the throttle down and the left. Anyway, if one direction doesn't work, try the other. If it's to the left, then you probably need to check step #5. When armed, you should be able to give it a little bit of throttle and see/hear all the motors go! There was much celebration when this finally happened for me! :)
4. Calibrate the Hardware, again using the Mission Planner. It's a pretty easy, step-by-step exercise.
5. I have a Spektrum DX8 transmitter and found that I had somehow gotten some of my lever directions reversed, as was covered in the last post on this forum:
https://code.google.com/p/arducopter/wiki/AC2_sensorGU. I had to go through the DX8 Function List configuration steps to reverse my 'Aileron', ' Elevator', and 'Rudder' so that the roll, pitch, and yaw directions were oriented correctly (as indicated by the high and low PWM rates in the Mission Planner calibration). The first time I tried to fly it, since these were reversed, it was REALLY confusing. Once I found this post and got my DX8 straightened out, it made a lot more sense on my second flight :)
6. It took me a while to figure out which switch on my DX8 was my "Radio 5" to control the Flight Mode. It is the "Flap Gyro" 3-position switch. I had all of my Flight Modes set to "Stabilize" in Mission Planner / APM, so I wasn't overly concerned about it, but it was frustrating not knowing. This seems to be an example where the people writing manuals just assume that the person using the DX8 know this. Anyway, now that I got it figured out, I've setup different 2nd and 3rd Flight Modes to experiment with after I've had some more flight time on Stabilize. Note that the switch position number is inverse of what you would expect in terms of corresponding to the Flight Mode number. Meaning, switch position 0 = Flight Modes 5/6, switch position 1 = Flight Modes 3/4, and switch position 2 = Flight Modes 1/2.
7. Once you've calibrated the ESCs and the rest of the hardware on the copter, made sure your transmitter levers are oriented correctly, and have been able to successfully arm (and disarm!) your ESCs, you should be ready to attach the propellers. There's plenty of material online to help you figure out which propeller go on which arm of the copter, but I recommend the following since it also shows you HOW to attach the props, as well as discusses balancing the props:
https://code.google.com/p/arducopter/wiki/AC2_Props. Note that you MUST put these on very tight. The first time I fired up the ESCs with the propellers on them and started to ramp up the speed, one of the props came flying off! Fortunately, it went straight down so it didn't injury me or cause any damage, but definitely stay a safe distance away the first time you ramp up the propellers to full speed.
8. Just a recommendation, but the first several times I took my copter outside to give it "flight", I rigged up a tie down system with string to all four of the legs of the copter to make sure I didn't kill anyone and destroy the copter. I just gave it a little bit of slack in the string, like maybe a foot on each leg so that it could get airborne and I could experiment with the sticks for altitude, roll, pitch, and yaw. Next time, give it maybe 2-3 feet on each leg to let it get a little more height. This also gave me a safe/easy opportunity to adjust the trim on the levers. For instance, it was pretty easy to see that as the copter started to lift, that it was rolling to the left, so I could safely adjust the trim to level it out without fear of crashing or destroying anything. I haven't yet actually had a chance to got to an open field and try it without the tie-downs...maybe later today :).
Anyway, that's my experience thus far. Thanks again to everyone who provided advice and hints. I've clearly got a LOT more to learn about this, including just getting some airtime and experience, and then starting to learn more about the Mission Planner software and how to do autonomous flight. But, in the meantime, at least I've now got a little bit of success under my belt to keep me energized about moving forward!