Madeira is most quickly reached via air. The main airport is the Santa Cruz Airport (FNC) which has a good frequency of flights from cities in Portugal and the rest of Europe.
The best way to reach the island of Madeira coming from Portugal is via a 90 minute flight to Santa Cruz airport from Lisbon.
You can also arrive to Madeira via ferry, however this form of transportation is seasonal.
Getting around locally is also convenient, with taxi and bus services from the airports and port areas available.