Dojo is included with the ArcGIS JavaScript API so there is no need to host/reference/install it. When you include the script tag referencing the ArcGIS JavaScript API, you get access to the full Dojo toolkit version.
To find the version of Dojo used by a particular version of the JS API, on a page that includes the JS API, open your browser's console and copy/paste the following:
[dojo.version.major, dojo.version.minor, dojo.version.patch].join(".");
That will print a Dojo version like "1.9.1". There's also a slightly longer AMD-compatible version that does not rely on globals:
require(["dojo"], function(d) { console.log([d.version.major, d.version.minor, d.version.patch].join(".")); });