Before following the instructions on this page, please complete section 'Install ROS core system' described here.
The ROS community has spent a lot of time setting up useful tutorials to get new users started with the software. These tutorials are a great and entertaining way of getting to know ROS. Most of them can be found on http://www.ros.org.
We also recommend new users to follow at least the basic tutorials. Afterwards, one can look at the more specific tutorials on a need or interest basis. And, as always, practicing in an own project improves learning. Have fun! :)
The basic tutorials of ROS can be found here. Before groovy, this was a (rather too) short list of pretty basic tutorials. Now, it has grown to a very respectable size. We recommend you cover
For first time users we recommend to stick with one combination of 'your favorite programming language' (C++ or python, where not all packages provide python-tutorials) and one build system (catkin or rosbuild, where catkin is the new ROS buildsystem of the future). For right-now we recommend you to use C++ and rosbuild.
Additionally, you should also familiarize yourself with:
Afterwards, it is always a good idea to revisit the tutorials to also learn how to use 'your not-so-favorite programming language' and 'the other buildsystem'. ;)
The built-in search of ros.org helps you finding packages released in ROS. You can find it at the top right of the website.
Let's say we are looking for the tutorials of our favorite simulator gazebo. Use the search to navigate to the gazebo package documentation page (gazebo, for those who want to cheat).
On this page you will find a blue box named 'Package Links'. These link to various useful resources about the package, such as the API an external website etc. There should also be a link to tutorials. Any well-documented package should have such a Tutorials link on its ros.org webpage.
Click on it. Et voilà, you found the gazebo tutorials!
Depending on the focus of your work you will likely want to look at tutorials covering very specific software packages.