The Metro Transit Hiawatha Line runs between the Mall of America, the airport (both terminals), and Downtown Minneapolis. Trains run every 7-8 mnutes during rush hour (6-9 a.m. and 3-6:30 p.m.), every 10 minutes midday, and every 15 minutes during the evening.
A day pass runs $6 and can be purchased at ticket machines located at each station. The trip between the airport and the mall takes about 12 minutes, between the airport and downtown takes about 27 minutes, between the mall and downtown takes 39 minutes.
Most hotels in Bloomington offer free shuttle service to the Mall of America. If you're coming to shop, that's great. You can even take the Metro Transit Hiawatha Line if you want to get from the mall to downtown Minneapolis. But if you want to explore other areas (including wonderful St. Paul), I'd recommend renting a car.
There are several car rental agencies located (conveniently) at the airport. Driving is easy - roads are well marked.
I'd also recommend bringing your own GPS and child seat. We rented from Alamo. Book as far as possible in advance for the best rates.