What does "programmatically" mean here?
You can start with "man 3 acl", which gives you the C-callable API for manipulating ACLs. For reading ACLs, you want to start with calling acl_get.
If you are in the kernel ... life is significantly harder. There is documentation of the syscall level in "man 9 acl".
On the other hand, if you are in a high-level programming language (shell scripts, perl/python), it is probably easier to use the getfacl command (see "man 1 getfacl"). I know that Python has a specific ACL library (with a non-obvious name, it's not as simple as "import sys.acl"), which can be used to build and decode ACLs. When I was a file system developer I used that for interfacing, but that was ~10 years ago. I just did a quick search, and there are several python libraries, and I don't know which one I used.
