Edit: As of February, 2020, there's now a first-class UI for automatically mounting Drive.
First, open the file browser on the left hand side. It will show a 'Mount Drive' button. Once clicked, you'll see a permissions prompt to mount Drive, and afterwards your Drive files will be present with no setup when you return to the notebook. The completed flow looks like so:
The original answer follows, below. (This will also still work for shared notebooks.)
You can mount your Google Drive files by running the following code snippet:
from google.colab import drive
drive.mount('/content/drive')
Then, you can interact with your Drive files in the file browser side panel or using command-line utilities.