I have created a file, admin, that I want to assign to a group, admingroup, and later on give a specific user, adminuser, exclusive access to that file but I have no idea how.
This is very easy in POSIX based systems.
chown adminuser:admingroup admin
That will make the owner of the file specificly adminuser and the entire group admingroup.
Then you will likely want to:
chmod a-rwx admin
chomd ug+rwx admin
That will remove all permissions from admin and then give user and group access to read write and execute the admin file.
This is a very decent tutorial on file permissions, though there are better ones. This should get you started though.