To change terminals at MSP, you need to take the light rail line one stop. It operates 24/7 between the terminals and there is no charge to just ride between the terminals. I've even seen people board with rented airport baggage carts, although please don't try to use them on esclators, use elevators instead. Trains run ten minutes every ten minutes during the business day and every fifteen minutes at most other times. The station is a long indoor walk at Terminal 1 (Lindbergh) from the baggage claim area and even farther from the check in counters.

If you have no luggage to check and either have printed your boarding pass or have a DL eticket and can use the kiosks to check in/print documents, then upon arrival at Terminal 1 via the light rail train, you should follow the signs to the skyway security checkpoint to save time (short lines, but nude-o-scope operated sometimes).