By Tube:
The closest Westminster Station is a 4-minute walk away.
By Train:
Travel to one of London's main railway stations. If you're coming from other parts of the UK, you'll likely arrive at London Victoria, London Waterloo, or London Charing Cross. From London Victoria, you can walk (about 15 minutes) or take the District or Circle line on the Underground to Westminster Station. From London Waterloo, take the Jubilee line towards Stanmore, getting off at Westminster Station (just two stops). From London Charing Cross, it's just a 15-minute walk across Trafalgar Square and down Whitehall or a short tube ride (one stop on the Jubilee line to Westminster Station). Once you exit Westminster Station, Westminster Abbey is just a short walk away. You can see the Abbey as soon as you step out.
By Bus:
There are numerous bus routes that pass Westminster Abbey. The bus services will be 11, 24, 148, and 211. You can get on the bus at the Parliament Square stop, which is directly adjacent to Westminster Abbey. From the bus stop, Westminster Abbey is just across the street, easily recognisable by its iconic structure.