Quick reply had me stumped too at first!
The instructions in the box say something like "please click one of the quick reply buttons in the posts above to activate quick reply". So you can't just type into the box - you have to scroll up the page, find a post you want to reply to, and click the "quick reply" button inside it. The button is in the bank of three buttons on the right (quote, multi-quote and quick-reply). Moderators will have an extra button, "edit post"
Then as Phil says, once the quick reply box has cleared, copy the location (url) of your photo to your clipboard, and then click the little yellow box of a sun and mountains just above the quick reply box. A pop-up will ask you to enter the location of your image. Paste in the location of your image that you just copied and click OK, and voila! You should have the image code inserted into your reply. Preview your post to check it dsplays correctly and then Submit your post to share your piccies!
A bit user unfriendly at first, but you'll soon get the hang of it!