Walnut oil is made by crushing shelled walnuts to a thick paste, then filtering out the oil from the solids. Unlike neutral oils meant for cooking, walnut oil has an intense walnutty flavor and is best used for finishing dishes. Try it drizzled over hot steamed green beans or asparagus, or in a vinaigrette for green salad or potato salad.
The best walnut oil producers roast the nuts before crushing to give the oil a toastier, nuttier flavor. Also, look for walnut oils made from the first pressing (similar to first-press olive oil), which has more flavor than subsequent pressings. If you can, taste the oil before buying: its flavor should remind you of fresh roasted nuts.
Walnut oil is prone to rancidity if it's exposed to the air for too long, so buy it in small quantities, seal it tightly after opening, and store in the refrigerator.