Buses: the workhorse, if you read the direction
Buses reach everywhere, run often and cost little. The catch is that outbound and inbound stops differ and stop names come in Portuguese and Chinese. Confirm the direction before boarding and carry coins or a topped-up e-payment method, as drivers generally do not give change. Peak-hour buses are packed and unkind to large luggage.
LRT: useful, but not everywhere
The Taipa LRT line links Taipa, Cotai and the checkpoint area — clean, punctual and a good way round traffic — but most of the peninsula old town still needs a bus or your feet. The network and its extensions keep changing, so look at the current map and operating hours before you travel.
Resort shuttles: free, and yes you may use them
The major resorts run free shuttles from the checkpoints, ferry terminals and city points, and they are open to people who are neither staying nor gambling. In practice they work as a free express network: checkpoint to Cotai, Cotai to the outer ferry terminal. The trade-offs are resort-door-only stops, early last services and holiday queues.
Taxis and walking
Taxis run on the meter, with surcharges for the bridges and for Coloane, and extra for luggage; in rain, after shows and around shift change they are effectively unavailable. Confirm the driver knows the destination before you set off and have the Chinese or Portuguese name to hand. In the old town walking often beats riding — but do not drag a suitcase up the calçada.
The cross-border leg
The Border Gate, Hengqin, the HZMB and the outer and Taipa ferry terminals each have their own operating hours and onward links, all of which shift with holidays and weather. Treat schedules, checkpoint hours and ticketing as things to verify on the day, and keep slack in your final leg.