It looks like most people answered your question as if you wanted to do un-licensed childcare, but I didn't get that from your post? Maybe I am wrong??
To get licensed (I am licensed in Hennepin county but I am sure its fairly similar all around the metro), look online for your county ..heres the place, but for some reason my links are not working wherever I copy them today!
http://www.co.ramsey.mn.us/hs/childcare/index.htm
But usually there is an orientation meeting (large group type) and then you can get all sorts of information and packets....and if you wish to pursue it further you fill that stuff out, send it in and they contact you about a small group meeting for more detailed stuff...then theres alot of getting your house up to code, fire Marshall inspections, some training to do like CPR, First Aid, SIDS and Shaken Baby(its ridiculous really how little they require). Other stuff is a good idea like contracts and policies, taxes and recordkeeping...alot of business stuff.
Getting licensed for your whole house is best if you can. Many counties around the metro now are pushing this rule that since your own children count on your license, they have to be in compliance with all of the same rules...so if their rooms are NOT licensed areas of the house, they cannot be in them during business hours...etc...something we are hearing more about. Once licensed...join a neighborhhod group! They are a great resource for networking, possibly mentoring and likely they have a referral network which can help you get clients.
As far as cost..not sure in your county, but its $130 here in Henn Cty...a few years ago, it cost nothing, but of course budget cuts changed all of that, but thats ok...most business pay a fee for licensing, we should be no different I suppose and its not that steep, after all...certainly could be worse!
Good Luck!