The application for the 2012 season is here (PDF).
Your application and fee should be returned directly to Arlington's Dept. of Parks & Recreation before March 31. Membership for 2012 is limited to 20. If there are more than 20 applicants, returning gardeners will have preference, and the remaining slots will be allocated by lottery after March 31. If you are not chosen, your fee will be returned.
If there are fewer than 20 applicants, the remaining slots may be filled on a first-come, first-serve basis, up until May 1st.