Monaco does not have an international airport. The closest international airport is Nice airport. Bus #110 runs about every half hour between the airport and the Monte Carlo Bay Hotel.
From Nice to Monaco, trains run about every half-hour. Try to avoid rush hours when it's sure to be standing room only and there are often delays.
Check schedules and buy tickets on thetrainline.
Buses 100 and 112 link Monaco with Nice's Port Lympia. There is no bus station in Monaco. There are several stops as the bus traverses Monaco on its way to Menton: Place d'Armes, Train Station, Monte Carlo Casino. Services are handled by Zou.
See details about a day trip from Nice to Monaco
The most scenic approach to Monaco is via the Moyenne Corniche which winds along high above the coastline. It's also a good way to avoid the traffic on the A8 motorway, especially during rush hour. On the Basse Corniche traffic can be heavy during the day.