Can the original "Age of Empires 2" be played in two-player mode, so I can play against a friend (and a few computer-driven societies)?

According to the website, Age of Empires II: Age of Kings supports multiplayer through both wireless and LAN. There is a place in the main menu called Lobbies, and from there you can either create a lobby or join your friend's lobby, and add as many computer players as you want from the game.

You can also join online wireless lobbies through this website.

Given the age of the original game, you might have a few technical wrangles such as the original game using IPX. But then again, you're going to have technical wrangles just getting it running on modern Windows. Without knowing how you plan to so much as run the game, and on what OS, whether you plan to use DOSBox/WINE, etc, we can't give you any more details.