What is the very best way to clean a clear retainer?

White vinegar/H2O. White vinegar and water, 50/50. The acidic vinegar will break down the basic tarter and soften it so your tooth brush can remove it. Be sure to use white vinegar as wine or apple vinegar will color your retainer.
Eliminate bacteria. Try using one of the commercially available denture cleaners (polident, efferdent, etc) every day. Follow the package directions exactly.