Hi,
We got married in May 2010. Prior to our marriage I was working in LA for couple of months last year. After marriage me and my husband are staying in MN. I have no income from MN and my husband has income only from MN. We would like to know how should we file our taxes, Jointly or Separate?

You can file joint return.
For MN return, your husband is resident and will report all his income. You are part year resident and does not have any MN income.
For CA return, you are part year resident and have CA income. Your husband is nonresident and does not have any CA income. Your U.S. Tax Return: Working or Living in Two or More states

I would ask an accountant or tax preparer who knows the tax code and what will get you the best breaks.