The Amtrak station is at the Union Depot in downtown Saint Paul.
Getting to Union Depot
Uber/Lyft/Taxi - All the car services will drive you to Union Depot.
Bus - The 54 bus going north will stop at the Union Depot.
Light Rail - using light rail requires taking the Blue line from the airport into Minneapolis. Once there they must switch to the Blue line to St Paul and ride that train to Union Depot.