The ExAM Application can be found on the Salesforce AppExchange here. To install the App you should navigate to the previously mentioned URL.
On this page, you are able to view some information about the product as well as a demo, but considering you are currently reading a document on how to install ExAM you have probably already informed yourself. You will log in using your Salesforce credentials from the Org you intend to install ExAM in.
Now that you are logged in you will click on Get it Now.
You will then be prompted to choose what type of Org you are installing ExAM into. Just as Salesforce recommends we agree and suggest you test in a sandbox before installing into production. So you would click Install in Sandbox.
Now you will confirm the installation details as well as read and agree to terms and conditions and click Confirm Install.
You will then choose who to install this package for and click Install.
You will need to allow the App to have third-party access so you will check the box Yes, grant access to these third-party websites and click Continue. The app will take several minutes to install and you will receive an email when it is complete.
Now that you have ExAM successfully installed in your Org you should check out the ExAM Initial Use articles to assist you in configuring the App.