Analyzing spatial data is one of the most powerful features of ArcGIS. To use spatial analyst tools you will need to turn on the Toolbox. To do this click on the red tool box on the toolbar. Click on Analysis tools then choose what you want to do from here.
For more info on any of these specific tools consults the ESRI website.
Example: Open the buffer tool by double clicking on it. Select an input feature (what you want to buffer from) and an output feature class (where you want the data to go). The output feature class will often be in a geodatabase (ie CBGIS). Remember to back the database up before you change data in it. You may want to select a name like buffFormationName or some other similar methodology. Select a distance in feet or meters and choose a field to buffer from and select OK. This will run the buffer. Add the output feature class that you just made to your made and check to make sure it displays the data that you want.
For more advanced buffers you can choose dissolve and then fields to dissolve by.
Once you have done the buffer you can do buffers on other features and union or clip to show regions of overlap between various features.