Sant Cugat is a city near Barcelona, in Catalunya, a region in Spain (and France). It is common that you get here by hitchhiking. If you want to get into Barcelona, you can get a train ticket in any train station (better FGC stations) for 3€ simple ticket.
Note that this town/city is really close to Barcelona, so if you don't find what you're looking for, try Barcelona page.
South towards Barcelona
The fast way is by going to the entrance of C-16 in Camí de Can Gantxet, also called Túnels de Vallvidrera. 
Take BP-1417 at the end of Avinguda de Gràcia in the city of Sant Cugat . This road is a very common option for drivers who don't want to pay the fares of C-16 highway. The road goes all along the mountain and there's a very high viewpoint where you can get the most beautiful view of Barcelona. You can ask to the driver to let you there and then take another drive. This road is more commonly said La Rabassada. If you choose this option, get ready for curves (and very beautiful views! :D).
Take BV-1462 in Carretera de la Floresta in Valldoreix 
West/South towards Barcelona, Tarragona, Valencia or East/North towards Girona, France
You can go to any of these directions by taking AP-7, there are two good spots:
The first is close to the city center. It's a roundabout on the North of the city, at the end of Avinguda de les Roquetes . This spot is good to go to both directions
The second is near Hospital General, on the frontier with Rubí in the Carrer de Josep Trueta, , this spot is better if you want to go to Barcelona, Tarragona or Valencia, but there might be people going to the south. Be careful by crossing the road, cars in that spot might go very fast. This spot is very far, you can get there by taking line bus 1 (L1) direction Mas Gener (L1 - Direcció Mas Gener), it costs 2€ simple ticket. So, it's useless unless some driver has let you there, or you live near that spot (like the editor of this page).
If you want to go to Barcelona, it's better to use the "South options" because almost every car is going there.