It is indeed possible to upload directly from your computer to the forums (not for profile posts and sigs, though). But for normal posts, simply tap the image icon on the toolbar and just drag and drop your image.
Alternatively, if you do need to use a file sharing site (this also works on sigs and profile posts), Imgur is a popular choice on these forums. It's the one I use, personally.
Alternatively, if you do need to use a file sharing site (this also works on sigs and profile posts), Imgur is a popular choice on these forums. It's the one I use, personally.