You install Proclaim! like any other Joomla! component. Be sure that you are running the latest version of Joomla. Proclaim! version 9.x is designed to run on Joomla versions 3 or higher.
Proclaim! needs the same minimums as Joomla. You will also need permission to write files and folders and create tables on your database. But if you can install other Joomla extensions then you can install Proclaim! too. If this is a fresh install, just download one of file packages we offer - either the package of everything, or just the component (though we recommend the full package). Log into your admin side and go to Extensions - Extension Manager. Install comes up by default, Browse to the .zip file and install.
Alternatively you can use the web installer from your Extensions - Manage - Install window. You may need to search for BIblestudy - the original name of Proclaim! We've had a tough time getting the Joomla Extension folks to grant us a name change!
The installation will take a while so be patient. You won't see any messages until it is all finished. Quite a lot of happening so don't be alarmed. Once the setup is complete you will see some feedback on whether the install was successful and if the css file needed to be created.
At this point you should look at the configuration articles to see how to set up Proclaim!