There is a direct bus between Marco Polo airport and the Piazzale Roma, on the west bank of Venice operated by ATVO Starts twice an hour, takes 20 minutes The buses run from the airport till about midnight but stop sooner on the Venice to Airport route. The Piazzale Roma bus station is well served by vaporetti and water-taxis and of course, you can walk everywhere.
From Mestre, you can take a bus to Venice - Piazzale Roma. You must buy bus tickets from specialized ticket kiosks and vending machines, as well as tobacconists and newsstands.