Leon is well connected to Madrid by Renfe train and ALSA bus.
Best way from Madrid to Sarria is take the Renfe train. There is more frequent service from Madrid to Ourense and Monforte de Lemos so it might be worth taking the train there and then bus from either Ourense or Monforte de Lemos to Sarria.
1800
Leon
1801 This section describes transportation services in Leon.
Index 1800
1802 Leon Airport
1803 Leon Trains
1804 Leon Bus Services
1805 Leon Urban Bus Services
1802
Leon Airport
Leon Airport (LEN)
http://www.aena-aeropuertos.es/csee/Satellite/Aeropuerto-Leon/en/
1803
Leon Trains
Leon Renfe Station
http://www.adif.es/en_US/infraestructuras/estaciones/15100/informacion_000037.shtml
Renfe
http://www.renfe.com/EN/viajeros/index.html
Renfe FEVE from Leon to Bilbao
http://www.renfe.com/EN/viajeros/feve/index.html
1804
Leon Bus Services
Leon Bus Station
http://www.leon-virtual.es/autobuses/2-7-4-7.htm
Leon bus schedules
http://aautobuses.com/index.php/ciudad/leon.html
1805
Leon Urban Bus Services
Alesa
http://www.alesa-alsa.com/
1905
Sarria
Empresa Freire connects Santiago to Lugo. Most but not all buses stop enroute at the Santiago Airport. Monbus connects Lugo to Sarria. The transfer point is the Lugo bus station.
Sometimes it is more time efficient to take Empresa Freire bus from Santiago Labcolla airport to Santiago bus station (every half hour) and catch another bus to Lugo.
Monbus has buses from Santiago bus station to Monforte de Lemos and buses from Monforte de Lemos to Sarria.
Renfe provides service to Sarria on trains running between Monforte de Lemos and Betanzos-Infesta. These trains originate in Madrid, Barcelona, etc and terminate in A Coruña or Ferrol. Trains from Santiago usually require a transfer at A Coruña, Ourense, or Monforte de Lemos. If you plan to get from Santiago to Sarria ... use the bus.
Sarria Consello Transportation Page
http://www.sarria.es/index.php?option=com_content&view=article&id=109&itemid=132&lang=gl
Monbus
http://www.monbus.es/index2.htm
Empresa Freire
http://www.empresafreire.com/html/castelan/seccion0.php
Renfe
http://www.renfe.com/index.html