It can be a little confusing.
First you have to click "Go Advanced", in the quick reply window, to use the advanced editing mode.
Then scroll down and click "Manage Attachments"
Then click "Add Files" and then "Select files"
Then browse your computer, select the file you wish to upload, and click the "Open" button.
Then click "Upload files"
After that you'll see the file in the Attachments window. There will be a little box in the lower right hand side of the file icon. You need to click it so that a check mark is there.
Then click the "Insert Attachment" button.
Then submit your reply as per normal.