See
How to use ArcGIS samples
for help on compiling, setting up the debugger, and running the sample.
If the sample has associated data, you will find that the sample's zip file includes a "data" folder alongside the language folders.
However, you will need to update the sample to point to the location of the data once you have extracted all the files.
Start Visual Studio, open the solution, and compile the project.
Right-click the output .dll and register it.
Start ArcMap and open a map.
Select Layer Types (VB .NET) or Layer Types (C#) in the TOC.
Select a layer type from the combo box to filter the layers in the TOC.
Right-click a data frame node to show a context menu, which is the default.
Right-click a layer node to show a simplified context menu containing the layer zoom in, open table, save to layer, and properties commands.