How does the travel works in One Piece universe?
It's been revealed there are several ways to travel apart from traditional ships.  It's also been hinted that the islands range from prehistoric to scifi advanced, so there are methods yet to be revealed.    


For example, Rayleigh swam from the Grand Line through the Calm Belt to reach the Amazon's Island.  
Skypieans have been shown to have flying devices and shells that could propel.  
Amazons have been shown to use creatures to pull the boats.  
Blackbeard's boat is just a giant raft, implying they just use a sail and row. (Given the strength of the characters in this class, chances are that there were a lot of rowing involved)
Franky came up with Coup de Burst, which also lets them cross vast distances quickly.  
Several subs have been shown so far including Wapol, and the Heart Pirates indicating travel without need for waves. The Marines probably have access to this tech (at least, Z's Neo Marines did).  
More importantly, several fruits aid in propulsion. Ace used fire to power his skateboat.  Whitebeard could probably just cause waves even in the Calm Belt to propel his ships (and quite fast I might add, based on wave size and speed).  Dragon (though not confirmed how) was the reason for the gust of wind that helped Straw Hats escape from Loguetown. He may be using similar methods. Dragon also used to have Bartholomew Kuma, who can repel things and land them anywhere in the world.
Several characters, including Sanji, can use Moonwalk.