El Camino de Compostela

" ..... the quickest and easiest way to Sarria."

From where?

El Camino de Santiago, not, de Compostela. Anyway, my guess is you’d need to get to Lugo, Ourense, or Ponferrada, then take a bus to Sarria. Someone who has used public transportation in Spain may have a link to a bus service. You can also ask on any of the Camino de Santiago forums that are out there, including on Facebook.

The point about from where is well taken. Assuming its from someplace at a distance and involves flying with Madrid being a likely arrival city in Spain then there is a direct train from Madrid to Sarria. As I recall there is a trick to finding it in Renfe - maybe an intermediate stop on the train to Lugo?

Assuming you are flying in from elsewhere, it's easiest to fly into Madrid and take a train. You'll need to change at Ourense...a little over 7 hours travel time.
Santiago also has a good sized airport. You can fly there and then take a train to Ourense and then to Sarria. A little under 3 hours travel time.
I just walked the Camino in June/July...let me know if you have any questions!
If you are on Facebook there are several very good forums about the Camino you should follow...
Cofraternity of Saint James
Camino de Santiago
Hiking the Camino de Santiago & Then the World

American Pilgrims on the Camino is a very active Facebook community that can give you any answers relating to walking the Camino.. I will also suggest Camingas - A Buddy System for Women on the Camino..
From a 3 time Pilgrim,
Buen Camino