Taxi, limo's and the subway/Skytrain are your main options from the cruise terminal. Uber/Lyft is coming to the city, but I've heard there may be cruise terminal restrictions for them.
IMO... when you exit the cruise terminal, look at the taxi line. If the taxi line is short (less than 10 minutes), I would take the taxi. If there are three ships docking... expect long waits for a taxi and the Skytrain is the best option.
If your cruise terminal is super busy, leave the taxi line and head up to the street and walk to the Waterfront station to look for the Canada Line station to the airport. As you pass the Pan Pacific and Waterfront hotel, look back to see if there is a taxi line and whether you can board there.
Skytrain to airport?