With AFS, Access Control Lists (ACLs) are used to set access rights on directories (not files). (ACL ref: http://www.angelfire.com/hi/plutonic/afs-faq.html#sub2.04 )
First, display the ACL on the directory: fs la $directory
tweety@toontown $ fs listacl .
Access list for . is
Second, look at the ACL and confirm that your AFS-ID is either in the ACL or is a member of any group in the ACL. You can check group membership with: pts mem $afs_group_name
Third, examine the AFS access rights (ref: http://www.angelfire.com/hi/plutonic/afs-faq.html#sub2.04 ) and confirm you have the access rights needed.
To administer an ACL, you only need the "a" access right.
However, in practice, it's easier to have all rights: "rwlidka".
Fourth, confirm you have authenticated into your AFS cell and have an active token:
elmer@toontown $ tokens
Tokens held by the Cache Manager:
User's (AFS ID 9997) tokens for firstname.lastname@example.org [Expires Sep 15 06:50]
User's (AFS ID 5391) tokens for email@example.com [Expires Sep 15 06:48]
--End of list--
It is possible in AFS to authenticate into more than one cell.