People generally need to use an outside website to upload pictures, the most common is here: http://imgur.com/
Make an account, then you can upload your images to an album. If you would like the picture to display in your message you will need to use the rich text editor. In the top bar of the editor there is a small icon of some mountains and a sun in a square, if you have uploaded a picture to imgur, then you copy the URL (the stuff that shows up in the top bar of your screen when you are looking at the picture) and then click that icon and paste the URL into the box that shows up, then it should display the picture in your message.
Guide on using imgur:
Step one.
Open imgur.com and press upload images
Step two.
This thing will pop up, you must take a screenshot in minecraft first (F2 windows, F3 & crtl apple)
then press this
Step three.
This will pop up and you will need to direct yourself to the minecraft screenshots folder.
C:\Users\(YourUser)\AppData\Roaming\.minecraft\screenshots
Step four.
Copy the link url.
post it on the forums OR in game.
Shortcuts: CTRL + C = Copy. CTRL + P = Paste