Buses from Santiago de Compostela to Sarria

Empresa Freire operates buses from Santiago (and pick up at Santiago (labacolla) Airport) to Lugo.

Empresa Monforte (Monbus) operates buses from Lugo to Monforte de Lemos. The bus stops in Sarria in either direction.

Alternatively;

Empresa Monforte (Monbus) operates buses from Santiago to Monforte de Lemos.

Renfe operates trains from Santiago to Monforte de Lemos (you can also connect to trains to Sarria but the schedule usually doesn't work)

Concello de Sarria Transport page
http://sarria.es/index.php?option=com_content&view=article&id=109:transportes-y-horarios&catid=60:localizacion&Itemid=132&lang=gl

Empresa Freire
http://www.empresafreire.com/

Monbus
http://www.monbus.es/

There's just one direct bus from Santiago de Compostela to Sarria and it's in the afternoon and just on working days (from Monday to Friday). For info about schedules: www.monbus.es

Otherwise, you'll have to change buses in either Lugo or Monforte de Lemos as whariwharangi told you. Alternatively, you could make the route by train changing trains in Monforte de Lemos but, as whariwharangi told you too, check schedules. For train schedules and bookings, take a look at www.renfe.com You may need to make a separate search for each leg because the RENFE web isn't very good with options meaning a change of trains along the route.