Miami International Airport: For most visitors, take a rideshare or taxi directly to Key Biscayne: roughly 30–50 minutes depending on the Rickenbacker Causeway and downtown traffic, commonly about $35–55 before surge/tip. The budget alternative is the free MIA Mover to Miami Airport Station, Metrorail to Brickell, then Miami-Dade Route 102 over the Rickenbacker Causeway; allow 70–90 minutes with the transfer and expect standard transit fares (about $2.25 per ride). There is no airport-to-island express worth hunting for.
Fort Lauderdale–Hollywood International Airport: Use a rideshare, taxi, or rental car; it is typically 60–90 minutes to Key Biscayne and can be longer in rush hour, with a rough rideshare cost of $70–110. Public transport means multiple transfers through central Miami and is a false economy unless your budget is very tight and you have no schedule.