A recent update to the Google Drive desktop app allows sharing directly from the app. To use this feature, open up the desktop version of Google Drive and right-click on a file you wish to share. You should see a ‘Google Drive’ option, which will show ‘Share…’ and ‘View on the web’ links when you hover over it.
The ‘Share…” link will bring up a familiar page, one that looks a lot like the Share window from the web-version of Google Drive. This is an update that a lot of users have been requesting, especially those who compare it Dropbox (which has had a similar feature for a few years).