I need to be about to restrict our channel (#Domino) to only a certain group of users.

How can I accomplish that

Set a key by typing /mode #domino +k <some key> and then only give <some key> to the people you want to let in.

Alternatively, you could make it +i by typing /mode #domino +i and inviting users in.

Alternatively, private (+p) and secret (+s) are also modes that are available.
I'm not sure what the differences between those two are, but I do know that with the +s mode, your channel will not show in the channel list (unless the person requesting the list is an IRCop).

Unless I'm mistaked, +p is outdated and is basically replaced by +s. In either case, +p/+s do not prevent anyone from joining if they know the channel name. +i or +k would be the best method to keep people out.

depending on the network, +p and +s have different uses.
one hides the channel from /list, the other also hides it from /who's