Google has recently added to new helpful buttons to Drive. These two new buttons will help you organize your Drive better and help you search for files.
These buttons will show up when you are in Shared with me, Recent, Starred or your Search results.
When you are in your Shared with me page, these documents are not in YOUR Google Drive. To fix this, click the Add to Drive button shown above in the green box. When you click the Add to Drive button, the files are now added to your Google Drive. Now you can organize those files in your Drive into the folders you want.
The other helpful button is the Move to button shown below. Clicking the Move to button allows you to easily organize your files into specific folders. I have shown two different views.