You buy mounts from the Crown Shop button at the top left of your screen.
Click on that and the saddle button and you will see what is available. Some are crowns only but some toward the bottom of the page are crowns or gold, click on the gold tab to see how much they are and to buy with gold.
In addition to what Northlite says, some permanent mounts come only in card packs, also available from the crown shop. With these, there is a big element of luck -- no telling which items possible in a card pack will actually turn up when you buy it. If you want to be sure of what you get, buy the mount directly from mount section of crown shop. If you want to gamble, buy a pack.
Also, be careful to click on the plain saddle in the crown shop, and not the one with a clock on it. The one with a clock on it is temporary mounts.
