For more than one passenger a Taxi is your best choice. It allows you to go at any time you want (unlike the shuttles, which have more rigid schedules) and it costs $35 FLAT.
If you’re a group of up to five people or have many bags, you can even request a minivan taxi. It will still be $35 FLAT. Here are some numbers of recommended local taxi companies.
The cheapest option is to use public transportation. The bus that will take you to Miami International Airport is the “150 – Airport Flyer” – It goes pretty fast, it’s $2.65 per person, and it has an area to place your luggage. Here’s more info on riding public transportation in Miami.