The Vert.x documentation is organised into a few different manuals.
Get Vert.x installed and execute your first Hello World Vert.x example with the installation guide.
The main manual contains an introduction to Vert.x and deals with general concepts. It's highly recommended you read this so you get a good overview of what Vert.x is useful for and how it works.
Modules are a core feature of Vert.x which you'll need to understand to write effective Vert.x applications. The modules manual tells you everything you need to know about using and creating Vert.x modules.
We provide an in-depth API reference manual that describes how to use the Vert.x to do most things.
There's a different version of the API manual for each officially supported language.
We also provide generated API documentation (e.g. JavaDoc, GroovyDoc etc) for each API
Here's a library of other useful docs
Some other Vert.x resources
Documentation for Vert.x 1.3.1-final