The best method to move around Goa is to hire your own bike. Practically at every beach you will find locals hiring out motorbikes to tourists. You can hire one of these bikes for about 200 Rs per day (5 USD). Be careful not to hand over your passport or any other important document if the person renting out the bikes demand some sort of guarantee from you.
If you are not inclined on riding around on your bikes the next option is to hire a taxi. They can be easily recognised from their yellow colored number plates. It is advised to negotiate the charges before you start your trip in the taxi since most cabs in Goa refuse to charge by the meter reading and instead may quote any random amount.