[quote=@MacabreFox]
What would be the process to becoming a city guard? 
[/quote]

Adventure
Find archer 
??? 
Profit

Windhelm hosted the Stormcloak forces, but its own permanent forces are mostly the guards. In the next chapter, a militia organization called the White River Braves will be featured. These guys are active in Eastmarch and Whiterun, and do everything from coast guard duties to road patrols to shoveling snow. 

When the Dragonborn took over, he was set on making the biggest army on Nirn. So yes, there was a degree of conscription. But like in medieval times and the world wars, it was selective. Plus, having the legendary Dovahkiin as your poster boy tend to generate a lot of volunteers.