Here in NE Arkansas, I plant mine usually by the 2nd or 3rd week of March (just finished planting a week ago). I cut a seed potato into 3-4 pieces with an eye or two each, dig a trench about 6 inches deep, and plant each set 6-8 inches apart. I use some fertilizer one time in the trench before dropping the sets in. They will come up in about 2-3 weeks. I let them grow until well after blooming and hill one or two times. They usually start to yellow and die sometime in late May or June, and I reach in with my fingers and see how big they are getting before digging. This is the method my father taught me. Last year we planted 6 rows, about 30 feet long each, white, pink, and russet potatoes, and harvested over 400 lb. combined. This year I planted 9 rows, with the same amount of seed potatoes as last year, plus some we had left over from last year.
I have not tried a fall crop, we usually have all we can use from a spring crop.