Marriage licenses are issued by Vermont town clerks. If both parties are Vermont residents, you may go to the town clerk in either of your towns of residence. If just one of you resides in a Vermont town, you must buy the license in that town. If neither party is a resident, you may get the license from any town clerk in the state. The license costs $60 and is valid for 60 days from the date it is issued.  
Information about Getting Married in Vermont is available from the Vermont Department of Health.