The quickest way from Yaletown to Olympic Village is the Canada Line. Olympic Village Station is the very next stop after Yaletown-Roundhouse, so the ride is one stop. In good weather many people walk instead, along the False Creek waterfront.
One stop on the Canada Line
Board at Yaletown-Roundhouse Station on Davie Street, near Mainland Street, and ride in the direction of Richmond or the airport. The station order is Waterfront, Vancouver City Centre, Yaletown-Roundhouse, Olympic Village, Broadway-City Hall. Anything heading south from Yaletown gets you to Olympic Village first, so you cannot ride the wrong way past it. Starting from Vancouver City Centre adds one more stop.
Fares, frequency and any service changes are posted by TransLink. Check the trip planner and service alerts on the day, particularly on weekends, when work on the line sometimes changes service.
Walking along False Creek
From Yaletown the False Creek seawall runs east and south toward the Olympic Village area. The waterfront gives you views across the water and avoids the busy streets. If you have time for it, this is the pleasant way to go. Check a walking map for your exact starting point, because the length depends on where in Yaletown you set out.
Bus along the creek
TransLink route 50 connects Waterfront Station with Olympic Village Station by way of Granville Island, so it serves the south shore of False Creek rather than Yaletown directly. Route 15 also begins at Olympic Village Station and runs along Cambie Street to Marine Drive Station. Neither is the obvious choice from Yaletown, but they are useful if your destination lies along those corridors.
If you have bags or a group
For luggage, a stroller or a late evening trip, a cab to the door beats the transfers. The Vancouver taxi page explains booking, and the taxi fare estimator gives a rough cost.