Click the "New" button and select "File upload..."  Then a drop down window will open where you can select the file or files that you would like to upload. In this case, I will choose a file from the desktop.

Once the upload completes, the new document will display in the file menu (see above). As you can see, the document shows as a Google Doc rather than a Word file. I will now drag and drop a file to show how this works.

In the image above, I have dragged a file to the Google Drive page and it has started uploading. In this case I have chosen to upload the file as a Word document (unconverted).

You can drag one or more files at once for import using this method.

Now, you can see that there are two "Outline" documents, one a native Google Doc and the other a Word doc.

In addition to Office files, you can upload nearly any text, image, or video files for storage. Only Google documents can be edited within Google Drive, but it will store pretty much any file just like Dropbox that you can download and edit later.

So, there you are, your own personal College "Dropbox".