To post an image in a post, you need the file's internet address. This can either be achieved simply by finding the picture you want online, right clicking it and hitting "Copy Image URL" (In Chrome atleast, I have no idea if Firefox, IE (You are a horrible human being if you use this) or Safari share this option. You may have to go the long way around, right clicking the image, open it in a new tab and copy the URL from the address bar).
Once you have that, you can either just use the IMG button in the posts, and paste the image URL into the popup and hit OK, or you can manually enter the tag, as such: [img][/img]
Hence, example, using Wikipedia's 200px picture of Norway's Flag:
Note that as Invisionfree are silly, URL's are automatically converted into links, and the name shortened depending on length. But it shows the beginning and the end, whcih are the important ones. Remember that the file extension, the part at the end, which shows which type of picture, has to be one that Invisionfree accepts, I suggest using .png (Best) or .jpg (Horrible, but still decent).
How to post the image:
As you can see in the code block, the URL goes inbetween the two tags. This is the norm for most tags, except the ones that have an '=' inside them, which generally require some form of data (Size, Color, Alignment).
Here is how the picture looks when posted:ADDENDUM
To upload pictures from your computer to use here, simply use photobucket (Requires account) or Imageshack (Gives you a link already including the [img] tags with a linkback to Imageshack). Imageshack is probably easiest as long as you don't mind the linkback