The co-op works the same as in Saints Row: The Third. If you're familiar with that title, you know what you're getting into.
There's always a few extra co-op details to work out in a game like this so we made this handy Co-Op FAQ. It features two player co-op via online connection or system link. Saints Row IV is an open world murderbox full of entertaining, mindless distractions which are better enjoyed with a friend.