From older text descriptions and translations, to often comical results

http://imgur.com/gallery/MpRBy

Imagine describing a car to an illustrator over the phone in a different country without telling them the brand

The answer will vary by the painter, place, and "past" you have in mind, but my friend Daniel Marcogsy's has a very nice blog on Rubens drew a hippo in the 17th century: How One 17th-Century Artist Produced a Good Painting of an Animal He’d Never Seen.

Short answer: he had written accounts, not-great drawings from other people, but more importantly, he had an awful taxidermy of a hippo to go off of. He riffed on it quite a bit — you can tell he tried to make it more "realistic" even though he didn't really know what exactly what would mean. He did a pretty good job under the circumstances. You can see, in the painting, how much better the non-hippo animals are.

But the basic answer is: they largely had to rely on the accounts and previous drawings of others, or some other approach like a skin or taxidermy. Sometimes they did good jobs. Sometimes they didn't. In some cases, one can trace the elaborate evolution of one person's account as a sort of visual game of "telephone." Dürer's rhinocerus is the best-known example of this, and was copied and re-copied for some 300 years.

With improvements in printing came the possibility of making relatively static, immutable images that didn't need to be redrawn every time you wanted to recopy them, and the fidelity of such images over time improved. Much is made of the impact this had on the work of natural philosophy and art in William Ivin Jr.'s very nice little book from 1969, Prints and Visual Communication.