The airport is ~35 minutes away from the city. You can take the Airlink 100 buses, the latest bus stop of the Airlink 100 is ~15 minutes walking from the venue, so once you get to Edinburgh you need about 1 hour to get to the venue.
More information on this link.
Waverley Train Station is in the city centre and 15 minutes walking to the venue.
Edinburgh Bus Station is in the city centre and 23 minutes walking to the venue.
Main locations of the event are marked with a star.