The first step in developing with Unity is, well, installing Unity. Head on over to http://www.unity3d.com/unity/download and click on the giant blue button, as seen in the following screenshot; this will begin downloading the installer for Unity. It's a fairly large file, so expect to wait a little while for it to finish.
Once it finishes downloading, locate the installer file and run it. Follow all the prompts that you see, with the end result (hopefully) involving the installation of Unity.
After a while, you will see a screen like the preceding one. Go ahead and tick the Activate a free 30-day trial of Unity Pro box and click on OK. The installation of Unity should now be complete.