The entire concept of "training" as a way to turn common men into soldiers is a very modern one, and our idea of basic training or boot camp, a weeks-long isolated training ground that would teach a soldier everything they would need to know as a typical grunt, only really materialized in the 20th century. The closest early modern practice was the recruitment depot, a camp that would teach things as basic as the position of attention, how to march and step, basic formation drilling, and "dry" recitation of the manual exercise, the drill of loading and firing by the numbers. It served as a very introductory phase of a soldier's experience, as well as an introduction to military style authority and discipline. It was, in concept and in execution, much less rigorous and comprehensive as modern basic training, for any branch in the western military tradition. I explain this more in this old answer here.

Part of the reason for this is that training wasn't viewed as the difference between a seasoned, reliable soldier and a raw recruit, experience was. Training means nothing if a soldier cuts and runs at the first fire, or clumps up into tight groups and fires when they're supposed to advance, or charges when they're supposed to retreat... you get the idea. Experience, on the other hand, was thought to keep a soldier steady and unflappable in battlefield conditions and, far more importantly, during entire campaign seasons and during times of deprivation or hardship. Battles are only the most visible expression of armies; the day-to-day challenges of weather, sickness, exhaustion, diet, exposure, confusion, shortage in clothing, shelter, equipment or materiel, to say nothing of how these would be compounded by bad or indifferent leadership, could not be replicated in any kind of training ground, and so outside of the recruitment camp, a soldier would be continually reinforced in military discipline while on their post or on campaign. Drilling varied from post to post and army to army, but generally, your drill would likely compose of little more than formation drill at the company size, and practice of the manual exercise, or serving a gun or riding a horse if you were in the artillery or cavalry. At the post, you would learn your specific duties on the job.

There were practical reasons for this, as well. Prior to the 20th century, there were few large state armies, outside of times of large-scale war, and the troops that were embodied were often far apart and somewhat isolated. It meant that the only time that soldiers might drill in a body larger than the few companies a single post might hold was during large-scale war games or literally on campaigns. Special tactics, peculiarities of the drill book or practice in specific formations would likely be done on campaign, and not in a separate training ground. I go into more detail about this here but I'll copy a bit by way of highlight:

"Militia and regulars only received battalion-level training under their commanders on the march, as they set off to their campaign objectives. William Henry Harrison specified a training focus as his army marched to recapture Detroit in late August, 1812:

The commanders of the several corps will immediately commence drilling their men to the performance of the evolutions contemplated by the commander-in-chief, for the order of march and battle. The principal feature in all these evolutions is that of a battalion changing its direction by swinging on its centre.

Harrison was himself a veteran of Anthony Wayne’s Legion, and the training methodologies had clearly made an impression on the young officer. In the Tippecanoe campaign, his militia officers pointed out that both regulars and the militia “were brought to a state of perfection” in the course of the campaign.

It is clear that times of active large-scale conflict was the only time in which meaningful training could be done with bodies of troops larger than a few companies at a time."

The War of 1812 also saw one of the more famous expression of regular, intensive training in Winfield Scott's regiment prior to the Battle of the Chippewa, which brought about the somewhat famous (and likely apocryphal) cry from the British commander, who spotted Scott's troops in gray coats due to a shortage of blue wool and assumed that they were "mere militia." But on seeing their regularity, their steadiness, and their clockwork evolutions under fire, cried: "those are regulars, by god!"

The utterance was likely fictional, as Scott's 1864 autobiography is the first recounting of that particular reaction, but it does point to a pertinent point: Scott had drilled his men for up to ten hours a day, every day for weeks before the battle. it is notable because it is so highly unusual - and Scott himself oversold the results throughout the rest of his life.

So, what were they taught beyond shooting and formations? Well to start, they might not even be properly taught shooting, but the manual exercise without firing, the process of priming, loading, and firing. If they were lucky they'd practice with blank charges, and they might fire live shots a handful of times. But beyond formations, they would be taught marching and evolutions, how to wheel in good order, how to march and countermarch, how to form a line from a column and a column into a line. But this is the kind of thing that would be taught on-post, and likely not at a recruitment camp. Recruitment camps would teach the bare, basic, absolute smallest-scale elements: the position of attention, the length of the step, the facings, and the manual exercise.

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Sources

Redcoat by Richard Holmes covers this quite well.

You can read Winfield Scotts autobiography here