Who administers the test depends on which one you choose. Lots of people use the Peabody test which has to be administered by someone specially trained, but is a really relaxed experience as tests go. However, there are tests you can administer at home too.
You need to test once a year after your child reaches age 7, but you don't submit the results to anyone.
If neither you or your dh has a bachelors/teaching certificate, they require quarterly report cards which would be a PITB, but aside from that the Minnesota homeschooling laws aren't bad at all.
Here's a link to MHA's website:
http://www.homeschoolers.org/minnesota_law_and_forms
ZM
(to be clear, I don't live in Minnesota, but I do live very close, and we're considering moving there soon).
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