Taxis from the airport to the center cost M$160 (shared taxis M$70 per person); buy tickets at the taxi booth inside the terminal. Going to the airport, some street taxis (ie those not called from your hotel, which are more expensive) charge M$150; penny-pinchers can try taking the hourly bus to Chiná (a village outside Campeche; around M$15) from the market, and getting off at the airport entrance, then walking 500m to the airport doors.
Within Campeche city, taxis charge M$30 to M$60; prices are 10% more after 10pm, and 20% more from midnight to 5am.
Most local buses (around M$7) have a stop at or near the Mercado Principal.
Consider pedaling along the malecón; get bike rentals at Kankabi' Ok.
Drivers should note that even-numbered streets in the centro histórico take priority, but go slowly until you get the hang of the cross streets.