From a long line of Southerners, I can tell you that most of the time they are cut up in chunks and cooked in the pot with the greens and a bit of salt pork. Turnip greens are a prized southern dish, but in Pennsylvania, I was told "we throw those away and eat the turnips. I like to cut one or two up in small chunks and add to soups, especially a chicken taco soup.
One of my favorite recipes is the beef, or pork roast in Mark Sisson's Paleo cookbook. I use a cast iron pot, meat is rubbed with his seasoning mixture, covered with sliced onions, and covered to cook three hours in the oven, first hour covered, second hour uncovered, third hour covered. For the last hour, I cut carrots, potatoes, turnips, parsnips, etc. in chunks and dump that onto the top of the roast, then cover. You could also place the vegetables in a shallow pan or sheet, season, drizzle olive oil, toss and roast. Turnips are also good prepared like mashed potatoes.
Having lived in different areas of the US, I have learned that turnips grown in different soils don't taste the same as those I grew up eating.