Example with Postimage:
Go to postimage.org
and upload one (or more) image(s) from your computer:
You can have postimage automatically resize your image(s) if needed:
Copy the Direct Link into your post:
Add the "img" and "/img" BBCode directly before and after the link:
In your post you can select the complete link and press the "Img" button in top of the edit window. This will automatically apply the "img" codes correctly to your link.
If you uploaded multiple images you can select the following to include them into your post as thumbnails:
Select "Codes for All Images", "Thumbnail for Forums (1)" and "1 Line" (or "3 Columns" or 4 "Columns")
options and directly paste the code into your post (no need to add the "Img" codes yourself).