The way to reach Quadra Island from Campbell River is the BC Ferries sailing that lands at Quathiaski Cove on the island. You drive or walk on at the Campbell River terminal, so the only real planning is the sailing time and the lineup.
The Campbell River to Quathiaski Cove sailing
BC Ferries runs this route and the island terminal is at Quathiaski Cove. Sailings go many times a day, but the exact departure times change with the season and the day of the week. The BC Ferries schedule page for the Campbell River and Quadra Island route shows the current times, the crossing length and any service notices. Look at it the day before you travel, and again on the morning itself if the weather is rough.
Fares differ for foot passengers, bicycles and vehicles. The fare table on the BC Ferries site is the place to confirm the current amounts. Vehicle traffic can build up on summer weekends and holiday Mondays, so give yourself a buffer rather than planning to arrive just before departure.
Getting to the Campbell River terminal
The terminal is in Campbell River, and a driving or walking route from your exact starting point is easiest to get from a map app. Check the BC Ferries terminal page for the address, the vehicle check in advice and what parking is offered, because parking rules and fees can change and are not worth guessing at.
If you would rather not leave a car at the terminal, a ride from town is a simple answer. A local cab or a booked ride can drop you at the foot passenger entrance and collect you when you come back. Campbell River taxi covers that kind of transfer, and the taxi fare estimator gives a rough idea of cost before you book.
Before you leave the island side
Once you are on Quadra, services are more spread out than in Campbell River. Work out how you will get from Quathiaski Cove to your final stop before you board. If you are staying overnight, ask your host about the ride from the dock. Note the time of the last sailing back to Campbell River when you arrive, and write it down so it is not a surprise at the end of the day.
Weather and mechanical problems occasionally change sailings. BC Ferries posts service notices on its website, and checking them before you set out saves a wasted trip to the terminal.