Cuchulainn,
TMP basically uses a code called BB Code (or bulletin board code.) It's a little like HTML, but generally the "tags" are surrounded in square brackets. Since you can't put the code into posts without producing results, I've taken the liberty of posting a screen capture of a text file showing how it's done . . .
I have, in fact, inserted this image using just the code depicted. You can add images, links, and even formatting like italics and bold and lots of others. (The "bold" tag doesn't, to my knowledge, always change the text color, but it does appear to on this site.)
You will generally need to include the http business in front of the two slashes and your image files will generally end in jpg or something similar. (Not all sites accept all image formats, but jpeg or jpg is fairly standard.) But between these bookends your filenames may include lots of slashes and seemingly random directory information. All of this is necessary and often case sensitive, so it's wisest to copy and paste.
You can right click on most images and select "copy image address." It's usually about halfway down. If you left click in your browser's address bar it will typically highlight the full address so you can simply hit ctl+c. (Which is to say hold the "control" key and the c key down at the same time.) Once you've done one or the other of these you can "paste" with ctl+v (or control and v at the same time.)
As a small further bit of demonstration, here's what the example code produces . . .
symphonicpoet.blogspot.com
This is the Poetry of the Symphonic
stuff in italics
stuff in bold
Hope some of this helps.