The first couple of times I played against my wife we used the coffee table as well. Then I got a table that extends and gaming has not been the same since
May I suggest VASSAL for you? Not only for its capability to allow you to play solitaire (as you are doing now), but also for its large community of friendly gamers who would be happy to help step you through the game and learn the system. You could even watch some online games and learn that way as well.
You mention this is your second game, so perhaps you have already done so, but if you haven't, may I suggest you step through the example of play in the playbook and then continue that game. Really nice script that demonstrates a broad swath of possible orders and actions.
I've already downloaded VASSAL, and I think I'll definitely be trying it with CC:E. Is there an etiquette to observing other people's games? Do you just visit the lobby and ask to observe?