Make sure the picture is saved on your computer as a .jpg, .bmp or .png file, then click on the "Photos" button above the body of the reply. Make sure to also have the cursor on this screen where you want the picture to go before you click on Photos. That way you don't have it end up before a paragraph it's supposed to be after, or something like that. Just put the cursor in the spot you want the picture, like you're getting ready to write a new sentence.
Then click Choose Files on the page you are taken to when you click on Photos.
Then select the file you want to add and click Open (if using a Windows computer). In the following example, I used the default name for the snip I took, which is "Capture".
Then, after it uploads, click Done, and it will post in the message body.
Remember where you save your pictures. Screenshoots (pressing Windows + PrintScreen at the same time) tend to save in the Screenshots folder in your pictures. When using the snipping tool, you can choose where to save them. Screenshots save as a .png file by default, which is uploadable. Using the snipping tool they save as a jpg file by default (I think), which is also uploadable. The pictures must be under 2MB in size or the upload will fail. You can use Microsoft Paint to edit the pictures before uploading, if you need to.
The following may also help. It explains how to take a screenshot.