There is no train to Sant Feliu. Coming from Barcelona, the easiest options are the Sarfa/Moventis bus from the Estació del Nord (around 1h45, runs every 1–2 hours) or driving (roughly the same time on the AP-7 to Tossa exit and then the coastal road).
The closest train station is Caldes de Malavella on the Barcelona–Girona line, with a connecting bus into Sant Feliu (around 30 minutes). For air arrivals, Girona-Costa Brava Airport is 25 minutes by car (or 50 minutes by bus); Barcelona-El Prat is 90 minutes.
Once in town, everything central is on foot. Buses run regularly up and down the coast — line 21 to Tossa de Mar and beyond — and a small fleet of taxis is on the rank by the Plaça del Mercat.