You have a lot of options to choose from for transportation in Fortaleza. As with usual tourists though you will find yourself spending most of your time at the beach and just about 5 kilometers away from the beach. You will only find yourself going a bit farther if you would need to go to the airport and bus station. So going around will be an easy thing. But if you are one of the more adventurous types that want to explore the city and not just stick to the usual places then it will be beneficial to know your transportation options.
You can go anywhere in the city by bus. This is the most affordable transport option. A trip would just cost you R$2. It is also the most readily available as most bus lines offer trips 7 days a week. They also run almost the entire day, and the number of trips would decrease as the day goes on. After midnight you will find bus lines going having only one trip. There are bus lines that go around for 24 hours, like Circular ½ so no matter where you are and what time it is, you can still go around the city.
If you want to avoid crowds in buses and want a more private transport option then you can take a taxi. There are a lot of taxis around the city and they run on the same type of meter. Be sure to check that the meter is running after you get in. Most cab drivers in Fortaleza though are fairly honest. They can even be negotiated if you are going out-of-town.