We obviously have rather rigorous standards of fitness today, but how did that translate two to three hundred years ago? Much of it today seems to be based around cardio, was this true back then? Given that a lot of it was walking as opposed to running, was this still emphasised? Could, for example, people with asthma join the military? There are dozens of questions to be asked so this is a relatively open question and I appreciate any answers to any relevant questions!
The Austrian army of the Napoleonic era, in regards to its infantry, concentrated primarily on formation and firing drills (albeit dry-firing, the average line infantry private may have had as few as 10 rounds of ammunition for firing practice per year.) The length of service for an enlisted soldier was so long it was practically for life, discipline harsh, and as they would live with their regiment year-round it's not difficult to imagine that day to day life would be rigourous enough to keep them fit.
I'm currently away from home but can fetch sources tomorrow if needed. I can tell you more about the enlistment process when I'm back home, too.
Regarding training, Dover Publishing has released a facsimile version of Baron von Steuben's revolutionary war drill manual. It's a very nice copy. You can get it pretty cheap at Amazon, too.
It focuses primarily on firing drills, weapon familiarization, prompt reaction to orders (and the intonation those orders are to be delivered in), how the officers are to conduct themselves, maneuvering the regiment as one unit, etc. If I recall correctly, there's even a few sections on the proper construction of camps. Given Von Steuben's prior service in Prussia and Hohenzollern-Hechingen, one can assume general familiarity with the way training and organization was conducted in Europe at the time.