I take it that you want to eradicate stinging nettle from your yard or garden? Are you opposed to using herbicide?

Stinging nettle is a native plant to Michigan. It is host to beneficial insects. That said, it can really hurt! 

Herbicides can be effective in killing stinging nettle. It may require repeated application as the plants regenerate from the roots. 

If you are against using herbicide, you will have to be constantly vigilant in removing regrowth from the nettles. I would start by digging as many roots as possible. Then pulling or digging out any new growth as soon as you see it pop up. It might take over a year to remove the patch of nettles. 

You can also try mowing it/string trimming it down to the ground. Then cover the whole area with black plastic. Make sure the plastic goes beyond the nettle patch and that it is held down tight to the ground with rocks/bricks/logs/landscape staples. Leave the plastic down from now through next spring or summer. Between the heat this summer and no light, it should starve the plants of energy so they die. 

Be careful not to plant around the edges of the nettle patch. You may inadvertently move nettle roots and create new plants. 

Make sure that you do not let any plants go to seed.

This is not a fun or easy project. You may find that you cannot completely eradicate them in one go. A lot of our perennial "weeds" take years to eradicate.