Dig a pretty deep trench for your row, 10 inches or more. Scratch up the soil a bit and mix composted manure in with the loose soil at the bottom of the trench. The roots will grow down into that mix. I use manure for nitrogen, and add rock phosphate per the dispensing requirements "on the bag". The rate for manure is about 50 pounds per 20 lineal feet of row. Over the years, I have put doses of greensand at the rate recommended in the bag. You would probably be putting a pint of phospate and a pint of greensand in with the "mix".
Add a small amount of lime if you soil is calcium deficient. We had over limed our garden over the years and that brought the pH up to an alkaline level. Potatoes get "scab" in alkaline soil. Some of our potatoes had scab last year.
The soil tester kits at the garden center are probably good enough for pH and nutrient levels.
Seed potatoes are usually undersized. It is best to place them whole into the trench, about 12 inches apart. I go with about nine inches spacing. You could cut your potatoes and let them set out for a day before planting them.
I place the potatoes in the trench, then bury them in the soil from the trench. The row still will look like a trench. When the plants grow to 12 inches high, fertilize them, then bury them halfway with the excess soil on the side. When the plant grows another 12 inches, bury them with the remaining soil on the sides. The soil to keeps sun off the potatoes, else they get green. Green means solanum, which makes some people sick.
I fertilize with compost. Water your plants during the potato development period. Last summer was quite wet and our potatoes developed an unappealing "hollow heart".
If you have clay soil, you are going to have to mulch the plants with straw instead of burying them in soil like I do. I have not done that. There are articles on the internet about straw mulch. You can even grow potatoes in a barrel. I prefer to grow on the soil, where the water table can bring water to the roots.
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