Salsify is a root vegetable. It is sometimes referred to as "oyster plant" or "vegetable oyster" because people thought it tasted like an oyster.
The most common preparation method seems to have been frying. It is often included with other root vegetables like turnips and parsnips in flavoring stews and "stuffing."
From: Domestic Cookery, Useful Receipts, and Hints to Young Housekeepers by Elizabeth E. Lea, 1846. Page 50
From: Miss Beecher's Domestic Receipt Book by Catherine Esther Beecher, 1846 Page 81