Did Athens men have to enlist in the military?

Answer 1

Yes they did have

Answer 2

"Military service was a primary distinction of citizenship—a mark of status and often of wealth, as well as a means of attaining glory. Furthermore, the initiatives taken during the latter part of the sixth century to standardize the Homeric epics in written form fostered a broader interest in heroic subject matter. In Athens, military service was determined by a citizen's social and economic position. In the early sixth century B.C., the archon Solon instituted four classes defined by income and gave each class a proportionate measure of political responsibility. The second wealthiest class, the hippeis ("horsemen"), earned enough from their land to maintain a horse and so fought as cavalry; the third wealthiest group, the zeugitai, were able to afford the equipment of a hoplite; the wealthiest class, the pentakosiomedimnoi ("five-hundred-bushel men"), supplied the leaders for the armed forces; and the poorest class, the thetes, were hired laborers who served as oarsmen in the Athenian fleet, or as archers and light-armed men on land."

"Warfare in Ancient Greece", The Metropolitan Museum : http://www.metmuseum.org/TOAH/HD/gwar/hd_gwar.htm

Answer 3

Basically it was their lifestyle, the men grew up to be warriors. It could be liken to the national guard where they all would have trained for so many hours each day in times of peace.
When fighting was to be done they would go to battle.

They had slaves to do all of the work, like building and farming etc