The real question is: do you want to play
Age of Empires? The answer is not so simple. If you'd like to see the origin of the style that
Age of Empires II has, you can't go wrong; unfortunately,
Age of Empires has been far surpassed in playability by games that have come along since then, and it's hard to recommend for any reason other than reminisce value. It's not an inherently bad game--far from it--but there's much better stuff out there.
The concept of the game is intriguing. You pick one of over ten different civilizations to play as, each with differing specialties (faster build times, stronger troops, and so on). From there, you take them from the Stone Age to the Iron Age, improving their combat abilities and eventually wiping the map clean of your opponents.
Unfortunately, the actual gameplay more closely resembles Warcraft II than any deep Civilization-style game. In the end, most of the trappings of technology feel like just another tech tree, and unit rushes are still the easiest way to win a battle. While Age of Empires aspires to more, it never quite gets there.
You generally start out in the Stone Age. Your villagers subsist on hunted animals and picked berries, as it should be. Slowly but surely your civilization starts to grow, and as you build a dock and barracks you become able to build a number of different units. The various civilizations have only a certain selection of units, so there's some variety there as well.
Progressing to the next Age is simply an expenditure of resources, like wood and food and gold. Each Age gives you a number of new units and buildings to play with, but the old ones stick around. It should feel a little more epic than it does; as it is, going to the next Age feels like just another notch on the tech tree.
Controlling your units is simple enough, but the micromanagement required for successful campaigns is downright silly. Why don't your warriors fight when nearby locations are attacked? Why are your villagers complete imbeciles when it comes to finding similar work to do? The pathfinding is also pretty atrocious. All of these things have been fixed in games since the release of Age of Empires (and some before), making it hard to play nowadays.
There are a large number of playmodes, though. You can participate in a number of campaigns, which are mildly entertaining but generally take entirely too long to do. You can also go the single-scenario route, with prebuilt maps and empires. There's the requisite multiplayer, through the Zone. And my personal favourite is the random map generation, which lets you play on different terrains and really keeps the game spiced up.