What is the best way to get from Lisbon Airport to Faro? Are there any shuttle services?
Flying would be quickest, otherwise it’s a half day transfer. I presume you don’t want to stay in Faro, so if you are heading elsewhere on the Algarve such as Lagos, it maybe quicker to take the train or bus.
This 2018 online article lays out several options: https://www.tripsavvy.com/getting-to-lisbon-and-faro-1642547
I haven't made that trip, but there's a train line running from Lisbon to Faro. Rome2Rio.com indicates that the trains depart from Oriente Station, which is connected to the airport by a quick subway ride. Of course, you could also fly to Faro.
Check the rail schedules on the CP website. Trains are not terribly frequent.
There are also buses, and I'm sure there must be a company or two doing transfers, but that woul be more expensive.
If you are flying from Canada you could connect by air to Faro. The connection would not necessarily be in Lisbon. Aer Lingus flies through Dublin, British Air from London, etc. Faro is a fairly busy airport because of tourism along the south coast. A good search engine will do the research for you. If you want to visit elsewhere -- a stop in Lisbon, for instance, -- use a multi-destination search function to fly into Faro and home from Lisbon, connecting by land transport. once.