There are so many different ways to grow potatoes, in stacks of tires, in bags, or just so many different ways it is hard to get too specific. But I'll try some basic answers.
Do not use seeds. When you plant tomato seeds the genetics are so complicated, you have no idea what you will get. Usually it is not something you really want. Use eyes from spuds. Often the potatoes you buy at grocery stores are treated to keep them from sprouting, so it is best to get some from a gardening center or somewhere that sells potatoes specifically for planting. Sometimes, those potatoes are treated with some pretty nasty chemicals to get them to sprout, so don't eat the ones sold for planting. That is sometimes true for any seeds you buy specifically for planting, so don't eat the seeds you buy for planting. I'll let others chime in about how to get around that, but not eating things I buy specifically for planting is one of my rules for me.
There are many different varieties out there from fingerlings to funny colored ones. I'd suggest for your first attempt, you try a basic varierty. For a red potato, I'd suggest Red Pontiac or some other one sold locally. For the white ones, Kennebec is an old stand-by. I go by a local garden center (not Lowe's or Home Depot, but a true garden center) and get my seed potatoes there, usually for about $0.45 per pound. If you get them shipped, they will be a lot more expensive. The variety they have should do OK in your area.
I'm not talking about sweet potatoes in what follows. Those are totally different. Regular potatoes produce potatoes higher than the seed potato, so you want to give them room to grow higher than where the seed potato is planted. You can do that with tires or other methods, but I grow mine in the ground. I scrape out a trench maybe three inches deep, put the eyes in there, then cover them with maybe three inches of dirt. As they grow, I scrape dirt up around them to eventually create a hill maybe 12" to 14" high. You don't totally cover up the green plant. Always leave several leaves showing through. This gives them room to make potatoes and makes them fairly easy to dig.
A word of warning. The potatoes need to remain buried while they are growing. A potato exposed to the sun will turn green. This is caused by a substance that is dangerous for you to eat that is produced in sunburned potatoes. So just keep them buried so they are not exposed ot the sun.
When the potatoes start flowering, that means the potatoes are being formed underground. You can stop burying them deeper then.
Hope this helps some. Good luck!!!
Editted to add. I start mine when the worst danger of a heavy frost has passed. The can take a light frost, and if they are hit with a hard frost they should grow back. Potatoes are generally a cooler weather crop, so don't wait too late. I'm not sure what the right time would be for you.