To download a webform, go to the contextual link of the webform. Note that this one is the contextual link for the block. This is not the contextual link you want. If you move the cursor down closer to the form, another contextual link will appear with different options. 

This is the contextual link you want, with options for "Test", "Results", "Build", and "Settings". You can see the contextual link for the block right above it. 

On this page, you can see all the results (submissions) for this webform. In the secondary menu bar at the top, click "Download". 

Scroll to the bottom and select "Download" for a .csv to be downloaded to your machine. 

How to Download Form Submissions