Great question. Short answer: kinda expensive. Your classic Hollywood gunslinger-type would have been referred to as a "Shootist" during the 1860s-90s, and would not have been your average "puncher" or cowboy. A shootist was a person who took the time and money to develop their pistol skills, and to do so meant a considerable investment in ammunition. It also meant that this was their job: they were a professional hired gun. This meant that it was beneficial to their professional livelihood (and personal safety) to practice A LOT. I only bring this up because scholarship on this period is more or less in agreement that what we see in movies today, a quick-draw master with dead-eye aim, was a very rare individual (though they did exist). Your average puncher or farmer would not have had the time, and more importantly, the money, to develop these skills.

As it concerns specifics (the "how" in terms of the level of expense), it was enough to deter any but the most dedicated professionals from really developing their skills to the refined edge you might expect from Hollywood films. A box of 1000 rounds would cost you about $25, which equaled about half a month's salary for most working individuals of the day. Depending on where you where (New York vs. Denver) or what you did, this income would vary, but think of it like this. One box of 1000 cartridges (so maybe a month's worth of target practice) was about the same as what you would pay for rent that month. It was a lot.

[Sources, Daryl Jones, 'The Dime Novel Western'; Richard Slotkin, 'Gunfighter Nation'; Michael Denning, 'Mechanic Accents']