After 1858 they wrote to the mint and asked for them and included payment of face value plus a few cents extra for the "proofing fee" A silver dollar cost $1.08, a half was I belive $.56 In the 1880's you could buy a "Minor proof set" that cost fifteen cents and contained the 1, 3, and five cent pieces. In 1883 it cost twenty-five cents but it had all three nickels. You could also just buy the nickels for 18 cents.
During the 1860's if you wanted a gold proof you had to buy the entire set for $43. They would not sell individual gold coins.
There are copies of letters in the mint archives from collectors writing in and ordering the various coins.