Your trip will require three legs:
- MIA People Mover from the terminal to the MIA Metrorail station. Cost: Free
- Metrorail Orange Line (going to "Dadeland South") from the MIA Metrorail station to Government Center. Cost: $2.25
- Metromover from Government Center to one of the Bayfront Park stations. Cost: Free
Your destination station will depend on where you need to be. The Bayfront Park station is at the southern end. The College/Bayside station is closer to the northern end of the park (near the Amphitheater, Bayside Market Place, and the American Airlines Arena). If you're not sure where you are going, just pick a station. The park isn't that large.
Here is the website for Miami-Dade transit. The menu options on the left side of the page will show you information for both Metrorail and Metromover.
http://www.miamidade.gov/transit/metrorail.asp