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.
That will make the owner of the file specificly adminuser and the entire group admingroup.
Then you will likely want to:
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.