As Spring is a free, open-source game, distribution and promotion is as simple as directing someone to the Download Portal. However, as Spring's main game content is entirely free (both as in beer and as in speech), certain mods requires copyrighted Total Annihilation material, which can be legally downloaded/used only if you own the original CD-Rom. Since Spring supports multiple mods, and some of them are 100% free (both as in beer and as in speech), advertizing Spring/free mods is safe, althought TA-based mods should be not be publicly advertized for the aforementioned reason.
Spring Promotional Material
Clan SY has begun to create shirts featuring the spring logo, such as this one:
This is the only piece of promotional material currently available, but it should increase as the project nears completion
Community Promotion Initiative
Begun in early 2007 by community member Neddiedrow, the Community Promotion Initiative is an attempt to collect data and resources to make a concerted and widespread advertising push in the future.
The main forum on the plans is hosted by Smoth at: http://cs.selu.edu/~ssmith/BB/viewforum.php?f=35

