How can we go about applying for a 3 year multi-access Schengen visa so that we may travel to European countries?
Apply at the appropriate consulate. There's no way to guarantee that they'll grant you a three-year multiple-entry visa, but your visa application will be free of charge thanks to the freedom of movement directive (2004/38/EC), and the decision is supposed to be made on the basis of an "expedited procedure." So if they don't grant a multiple-entry visa, you will only have to endure minimal additional hassle.
The appropriate consulate is the one for your "main destination." For more information, see Schengen main destination.