I plant potatoes every year. I really like Russian Banana Fingerlings, they're my favorite. This past year I also planted Yukon Golds. They were good, but they're subject to some kind of blight where you get black hearts in some - ruins the whole potato

But they didn't all get it, so I had a good harvest. I don't grow a huge amount, I've still got fingerlings downstairs, but the Yukons are gone, I finished them off this week.
I dig a trench with a hoe about 10" deep and plant the potatoes in the bottom of that. Potatoes form on the stem
above the potato piece you plant, that's why you bury the stems as they grow. They flower (pretty flowers one some of them) and then die back, that's when you harvest them. Don't clean them off, let the dirt dry on them, and get them out of the sun - they'll turn green, you can't eat the green on them, it'll make you sick.
I'm not the expert potato grower, I'm sure others will pipe in with more advice.