Once you have installed and activated LCM for ArcGIS, the module can be found after the following steps. In ArcMAP, go to the Customize tab then Extensions. In the list that pops up, make sure Land Change Modeler is checked. After that go to the Customize tab again, and this time click Toolbars. Make sure Land Change Modeler is checked off here as well. After that, the Land Change Modeler toolbar with its one icon should pop up on the ArcMAP interface, simply click the LCM icon and the module will appear as a side panel and you will be all set to use it as you please.
Tutorial data for the Land Change Modeler for ArcGIS is installed during the installation and by default found in the Public folder.
Additional installation instructions can be found here: https://clarklabs.org/support/lcm-for-arcgis/.