My Jupyter Notebook has the following code to upload an image to Colab:
from google.colab import files
uploaded = files.upload()
I get prompted
Use this function to upload files. It will SAVE them as well.
def upload_files():
from google.colab import files
uploaded = files.upload()
for k, v in uploaded.items():
open(k, 'wb').write(v)
return list(uploaded.keys())
Now (sep 2018), the left pane has a "Files" tab that let you browse files and upload files easily. You can also download by just double click the file names.