There are two simple ways you can delete a file.
OPTION 1 - select a file by clicking the checkbox next to it. Then RIGHT click on the filename or row and select "Delete".
OPTION 2 - select a file by clicking the checkbox next to it (or click on the filename). Then HOVER over the row and a DROP DOWN ARROW will appear:
Then click the drop down box and various options will show up. Click the DELETE option.
A confirmation box will appear asking you to confirm that you really want to delete the file.
If you want to delete multiple files at once, this article explains how to select multiple files.