Sure. One caveat is that I'm doing this from desktop and haven't tried it from a mobile device. I think that should work more or less the same way but there are a lot of variables there. Anyway...
The initial screen lets you set a couple of parameters: you can resize the image if your original is oversized/hi-res and set an expiration if you only need it to be available temporarily. Mostly I assume you'd want to use "No expiration" for anything you're posting here but the re-sizing options might be handy. They contain descriptors (avatar image, thumbnail, message board etc) that make that pretty self-explanatory.
Then hit "Choose images" to select the one(s) you want from your local files. This uploads your image and gives you a choice of ways to link to it. Simplest one is the second, "Direct link." The way the TUD system works, if you just copy that link and paste it into your post, the image should automatically appear, as in this picture of my beautiful granddaughter: