From the SCQ airport, or from the bus station in Santiago, you can take a FREIRE bus from Santiago to Lugo:
http://www.empresafreire.com/html/caste ... cion3a.php
Then, in Lugo, you need to catch a MONBUS to get to Sarria:
http://horarios.monbus.es/
Do you have a working knowledge of Spanish? If not, here's how to navigate these 2 websites.
On the FREIRE website, under "Seleccionar Origen," choose either "Aeropuerto de Labacolla (SCQ)" if you'll be going from the airport, or "Santiago (Est. Autobuses)" if you'll be going from the main bus station.
Then under "Seleccionar Destino" choose "Lugo (Est. Autobuses)". Choose your date and you'll see a list of times and days for this route. Note that some of these buses are actually express and take 1.5 hours, versus some that take over 2 hours to get to Lugo.
On the MONBUS site, enter in "Lugo" in the "Desde" window, and choose the 2nd option that pops up ("Lugo EEAA")
Then enter "Sarria" in the box labeled "A".
Choose "Ida" (one-way ticket), choose your date from the calendar, and it will give you a list of times for the route Lugo --> Sarria.
Buen Camino!!