It is not possible to legally watch "Avatar" online for free. "Avatar" is a copyrighted film, and streaming it for free in the United States is a violation of federal law.
As of 2015, Web users can legally stream "Avatar" from Amazon Instant Video as a rental. This method is not free, and the fee depends on video quality. The high definition version of the movie is more expensive to stream than the standard definition version. Amazon Instant Video also offers "Avatar" for purchase and download, with different pricing tiers for standard and high definition.
Apple's iTunes store offers "Avatar" as a download as well. Apple only sells the high definition version, so there is only one price tier. It is not available for rental or streaming from Apple.