Place your image someplace like the public folder of Dropbox, and copy the public link to your clipboard.  Put the cursor in your post where you want your image to appear.  Click on the thing that looks like a picture of a tree in the header of the quick reply (second icon to the left of the smiley face) and a pop-up will appear where you can paste the URL of your image.  That should do it.

Other image hosting sites work, too, it's just necessary to have an external link so that the forum software can find the image on the web.

Really?  When I open my Dropbox folder, right click on the image I want, and then click on "Copy public link", the URL in my clipboard doesn't have any dl=0 at the end.  It just ends with the file name.

You're welcome.  I'm just passing on the information I got from someone (sorry, don't remember who) when I first tried to include a picture in a post.

I'm using the Dropbox folder on my desktop.  I'm not logged in.  I think the difference is that every image I want to share is in the "Public" folder within the Dropbox folder.  That folder got created for me automatically, so I assume you have one too.  It's meant for sharing. 

If I right click on a file in the Public folder, I get the "Copy Public Link" option.  If I right click on a file anywhere else in Dropbox, I get the "Copy Dropbox link" like you do.  With the "Copy Public link" you don't get the dl=0 stuff.

Ok, I visited the Dropbox help and discovered that on accounts created after Oct 4, 2012, Dropbox disabled the Public folder and made it a feature available only on their Pro and Business accounts.  So, if you happen to have a Public folder, it's easier to use it, and if you don't (and don't have a Pro or Business account) then you're stuck with the dl=0 ==> dl=1 method.