Harvest sweet potatoes before the vines are frostbitten. Frost on the vines can damage your crop, so if the vines get killed back by frost, cut the vines. Harvest the potatoes as soon as possible after cutting the vines because cold weather can adversely affect the storage time of sweet potatoes. In short, harvest 2-3 weeks before the average killing frost in your area. For me, this is now and a couple of days ago, I harvested my sweet potatoes.
When I planted sweet potatoes this year, I planted them in tall ridges of soil and covered the bed in black plastic. The sweet potato bed is pictured and described here: Planting Sweet Potatoes.
Gloves, hand trowel, digging fork, towel or sheet (optional)
To harvest, I pulled the plastic off in sections and pulled back the vines of each row of plants to expose the dirt. Working my way toward the plant, I pushed off the dirt with gloved hands. If your dirt had been walked on and has hardened, you will have to use a hand trowel or - very carefully - a digging fork. Try your best not to damage the sweet potatoes when you harvest them.
Depending on the variety, expect to find sweet potatoes both under the plants and between the plants and an occasional one as much as a couple of feet away in the perimeter of the bed. The variety that I planted produced mostly under the plant. See image below.
Dig around the sweet potatoes and carefully lift them out. In some cases, once enough dirt is removed, you can lift the whole plant straight up freeing the potatoes underneath.
When removing the vines, check them for sweet potatoes. If the vine touches a place that is (not quite sure how to word this) "friendly" such as a thickly mulched area, it can make sweet potatoes right there, right off the vine. See image below.
Break off the thin root parts that might be hanging off the potatoes and lay them on a towel or sheet or the surface of the ground to cure for a few hours.
After curing outside for a few hours, take the sweet potatoes and place them in a ventilated warm place, ideally between 85 to 90 degrees Fahrenheit. Allow the sweet potatoes to cure in the warm place for 10-15 days.
After the sweet potatoes are cured for 10-15 days, store them in an area that is cool, but not below 50 degrees Fahrenheit. Temperatures that are cooler than 50 degrees Fahrenheit will encourage the sweet potatoes to decay. Do not handle the sweet potatoes while in storage except to choose a few to cook.
Observations on production factors:
1. The one sweet potato plant that did not produce well was in damp soil.
2. The sweet potato vines that had the most spreading room made the most sweet potatoes. [Additionally, those vines were not cut back at any time during the growing season.]
Image below: Sweet potato vine spreading into the adjacent daylily and mint beds.