Parking information is available on the directions and parking page of the Minnesota State Capitol website from the Minnesota Historical Society. The accessibility page of the Capitol website has links to accessible parking information and maps. Parking rates are listed on the parking page of the Minnesota State Capitol Restoration Project website.
Keep in mind that parking is very limited during the legislative session (January-May). You may want to consider public transportation. Both the Metro Transit bus line and the Green Line light rail have stops near the Capitol.