I will specifically address the British system.
Recruitment was one of voluntary enlistment. That is to say, you cannot simply be dragged off by the government to server in the military. You had to sign up for it. This is not to say that the recruiting party couldn't mislead you or get you drunk and let you sign your life away. The enlistment bounty was a sum paid to recruits upon enlisting, however it was not uncommon for predatory NCO's of the recruiting party to coerce the new recruit into spending most of it treating them to drinks.
Recruitment from civilians was aimed at those of lower income and manual labour jobs or the unemployed. For example, a recruitment poster for the 14th Light Dragoons (I know you asked about infantry but the demographics for recruitment were largely identical.) states some of the possible enlistees
All you who are kicking your heels behind a solitary desk with too little wages and a pinch-gut Master - all you with too much wife, or are perplexed with obstinate and unfeeling parents.
There is a temptation to place a larger emphasis on the idea that recruiters were focused on tricking the foolish into enlisting or that large numbers were criminals. This is disingenuous, you don't start drinking or talking to a recruiter if you don't have some initial intention to enlist, no matter how small.
In 1795 the British government established recruiting districts to better manage and increase the flow of recruits in an attempt to solve a looming manpower crisis. There were 15 in England, 4 in Scotland and 5 in Ireland. Each was headed by an inspecting field officer with an adjutant, a Sergeant Major and a 'requisite number' of depot Sergeants. A year later a hospital mate was added to ensure the medical fitness of the recruits. A disproportionate number of the men assigned to regiments were Irish, due to much larger enlistment from the Irish militias. Incidentally not all recruits came straight from civilians, many actually came from militia units which had the great advantage of already being trained and tended to come in large 'batches' rather than the steady trickle of conventional recruitment. However this did have the disadvantage of drawing away men who would otherwise serve in the regulars to the militia units, who could not be deployed overseas.
The height for general enlistment was 5 feet 4 inches for general service, it was generally higher than that for the foot guards by about an inch or more. They also had to swear to be physically fit and that they did not suffer from fits or have a 'rupture'.
Training took place at the regimental depot, normally with the 2nd Battalion of a regiment (if it had one) or independently if the battalion was deployed overseas. Now. I'm actually struggling to find direct accounts of training by recruits. However I am familiar with the process by which recruits were trained, not all regiments trained in the same manner but the drill manuals are fairly consistent and differences are likely to be superficial. Individual experiences of training will likely vary based on the NCO's and officers training them.
Initially each recruit was instructed, without arms, individually on things like how to stand as a soldier, the facings, standing at ease, the step and halting.
Then, in groups of 3 or 4 they are instructed on the dressing of ranks when halted, mark time, the quick step, the side step etc.
Then in groups of 6 to 8 they were taught the quickest step, marching in file, and wheeling in a single rank.
With arms they were again individually taught on the positions of a soldier and the motions of a firelock.
Then as a group of 6 to 8 again on the more complex drills such as forming a squad in two ranks and wheeling in a platoon, platoon exercises and the firings.
For a more detailed read of this I suggest the drill manual that I list in my sources.
For the British drill was exceptionally important. The effectiveness of a battalion on the field was based largely on its ability to effectively manoeuvre and perform drill even when under strenuous circumstances. As such a man was not allowed to join the battalion until he was deemed skilled enough in the drill, as any man making a mess of it could disrupt the rest of the formation. Things like using drums to mark the pace of marching were also forbidden as the men could develop a reliance on it. The training reflected this attitude, with the recruits not trained on one particular drill for too long, even if they were terrible at it, as it could lead to boredom and frustration and permanently damage the training of the recruit.
Sources
British Redcoat (2) 1793-1815 by Stuart Reid
British Cavalryman 1792-1815 by Philip J Haythornethwaite