To see the lovely emirate of Dubai, via public transportation, you need a bus ticket and a metro pass. I’ll make it easy: buy the 25AED bus ticket at the green central bus station, behind Al Wahda mall, for a one-way seat on the comfortable red striped bus. Then, exit at the Ibn Battuta stop and purchase a silver, refillable, user-friendly Nol card. This card is the entry for Dubai buses and metro and can only be purchased in Dubai.
Use the metro (above ground rail) to get all around the spread out city of Dubai. Enjoy the malls, the Marina area, hotels and restaurants.