Valencia’s public transport system is excellent. The metro, buses, Valenbisi and taxis cover everything you might want to do. Cycling is very safe in the city because there are so many bike lanes.
You can pay for individual trips at the machines. If you want to take several trips, buy a 10-trip bono ticket. You can also buy a plastic card in a tobacconist shop, which you can top up at any tobacconist or newsagent/kiosk.
You can pay cash on buses. If you want to take several trips, buy a plastic card as above for metro. The plastic card can only be for metro or buses, not both.
This scheme is similar to the London ‘Boris bikes’ and superb value. A week’s use of the scheme is ~€15 and a whole year is ~€28.