What happens when you click the Download button? It should automatically download (or launch) Adobe Download Assistant(ADA) which will then do the rest.
Make sure that a security software is not blocking the launch/download for ADA, and that your user account has sufficient permissions to install software.
See http://helpx.adobe.com/creative-suite/kb/download-install-trials.html for detailed instructions.
Or watch a demo here: http://blogs.adobe.com/vikrant/2012/05/download-install-a-cs6-trial/
Also let us know what OS are you on. It'll helps folks to help you faster.