There are a couple ways of doing it. If you're uploading an image directly from your computer, there's an
Upload Attachments button next to the
Preview Post button on the reply page. These are only visible if you hit
New Reply; you can't see these from the Quick Reply window that appears under forum posts.
You can also use BBCode tags around an image url. This only works if the picture is already on the internet somewhere and therefore has its own link, but there are tons of sites out there like imgur that you can upload images to first to get a url.
Code:
[img]https://www.nedesigns.com/uploads/screens/4401/4401.png[/img]
The advantage to the second method is that the entire picture is displayed in the post, rather than a miniaturized version that you have to click on to enlarge.
The image below was inserted by using the code above.