Aerial view of the Edmonton International Airport by Thankyoubaby (CC BY-SA 3.0 License)
Now, before we get started, here's a mini geography lesson: The Edmonton Airport (YEG) is located in Leduc County, a municipal district that is just south of the City of Edmonton. So technically, YEG is not inside Edmonton but just outside of it.
1. Taxi / Uber / Lyft
The easiest way to get between Edmonton Airport (YEG) and Downtown Edmonton is by taking a taxi / Uber / Lyft. Taxis have been around for the longest, followed by Uber, and more recently, Lyft.
From my experience, the average cost between the airport and Downtown Edmonton via taxi or an Uber is approximately $45–$65, and the drive will take about 30 minutes. Whether you tip or not is up to you, I'd say.
I have not used Lyft, as it has only started operating in Edmonton very recently.
2. Edmonton LRT + Bus
Another way is to take the LRT (Light Rail Transit), which is part of the Edmonton Transit System (ETS). The southernmost LRT station that is closest to the Edmonton Airport is Century Park. It takes about 15–20 minutes drive to get from Century Park Station to YEG.
A map of Edmonton's LRT Stations by Thankyoubaby (CC BY-SA 4.0 License)
You could take a taxi or an Uber between Century Park and the airport, although I am not too sure how much it would cost. It should be less than what it would cost if you were to take it directly to/from YEG from/to Downtown Edmonton, but you should also factor in your time and how you would carry around the bags you have.
Alternatively, you could take Bus 747, which goes between Edmonton Airport and Century Park.
The bus trip will cost $5, and you can pay it in cash to the bus driver, or you can pay with an Arc Card, a reloadable card you can use to pay for public transit in Greater Edmonton. If you have this card, you can tap it upon entry and exit of the bus.
To take the bus from the Edmonton Airport to Century Park Station, exit through Door 8, cross the street where the taxis are, and you should be able to see a bus stop sign for Bus 747.
To take the bus from Century Park Station to Edmonton Airport, locate the bus stop sign for Bus 747 and board the bus from there when it comes.
Click here for the schedule of Bus 747 between Edmonton Airport and Century Park.
3. Drive to the Airport and Park
If you have a car, and you're flying out of Edmonton and are coming back, you could drive to the airport and park there on a daily, weekly, or a monthly basis.
This official Edmonton Airport webpage shows current parking rates and how you can make a booking.
There used to be shuttle buses you can book to get between the airport and the city, but as far as I know, they are not currently in operation.