I heard about Yacón, a tuberous vegetable cultivated in the Andes, and was wondering if I can grow Yacón in Minnesota.
Yes, you can, provided you have a warm and sunny spot - like where tomatoes would be happy.
Currently there are ongoing promising studies from the University of Hohenheim regarding commercial production in warmer regions of Germany, but many hobby gardeners report good success in home gardens. Yes, the plants rarely bloom and stay smaller than in their natural habitat, but 2 meters instead of 3 isn't bad and the yield of tubers is still plenty.
Note that neither the plant nor the roots / tubers are frost resistant.
Plant them in your garden after the last frost. Choose a well draining spot with plenty of sun and warmth. "Wet feet" can cause rotting. The fast growth needs lots of nutrients, so choose a fertile ground or add compost / fertilizer.
Once the first fall frosts have caused the stalks to wither, dig up the roots for the kitchen and store the core (the perennial rhizome it grows from, which will produce a new plant or can even be divided next spring) in a cool, but frost-free place below 10 °C, e.g. in slightly wet sand or peat like you would for storing carrots or overwintering dahlias.
If everything went well, you can take apart the overwintered core in early spring (February or March) and plant individual pieces ("eyes") in small pots indoors. Do not cover entirely, the eye should remain open. Plant outside after the last frost. Others simply wait and replant like for dahlias.
Overwintering is reportedly the most tricky part. If you are ok with possibly buying new tubers every year, you should still be able to get a good harvest.