The user only needs the execute bit present on a directory containing a file to be able to access the file. If the execute bit is set on the directory and the user has write permissions to the file he can edit that file. Without write perms on the directory he wont be able to create or delete files (even if he owns the file), but he will be able to edit them. Note though that without read permissions (only execute is set) the user wont be able to get a directory listing, he'll have to know the exact file name of the file to be able to access it.
So if our file is at dirname/filename.txt and user owns the file:
rwx--x--x dirname
User can edit dirname/filename.txt
User cannot create dirname/filename2.txt
User cannot delete dirname/filename.txt
User cannot ls dirname
rwxr-xr-x dirname
User can edit dirname/filename.txt
User cannot create dirname/filename2.txt
User cannot delete dirname/filename.txt
User can ls dirname
rwxrwxrwx dirname
User can do anything
NOTE
These rules do not apply if the directory has the sticky bit applied. The stick bit changes the behavior completely (the /tmp directory has the sticky bit applied).