Virtual Robotics
Even if you don't have access to a real Mindstorms NXT or EV3 you can also try your hand at programming a robot virtually using the following programs.
From the Mindstorms site Scroll down to the PC/MAC download and install. This is the coding bit of the software where you will write instructions for the robot. This is free to download and use. Note! Mac users will have an additional step below.
On a Mac, the EV3 installer may appear to fail but the software is in the launcher. You will need to then install an update to Silverlight so that the software runs.
Virtual Robotics Toolkit has a free trial period but can be purchased for $50 USD.
The help guide that goes along with the Virtual Robotics Toolkit is a good guide on how to write a simple program in the EV3 programmer and then downloading it to the virtual robot. Don't forget to press the Play button after you download the program to the EV3!