It is useful to remember that if a boat is flooding, the source is likely obvious. (True, if holed below the waterline the ingress may be inaccessible because of ceiling or TAFG and the highly theoretical exterior canvas patch the only resort. But that is very, very seldom the cause. And you probably sink.)
But usually it's a known hose of some kind, or a known hole of some kind--throughhull, sensor, stuffing box, shaft log and so on.
The first act is to instantly, aggressively and obviously, locate the water inflow. Never mind the radio and the bilge pumps and calling for help. Find the leak.
All typical leaks can be plugged, even in the face of water spurting in. The point is to do it, do it, do it. Nothing else matters.
Sounds like theory but I can tell you that over the years I have faced this several times. My 21-foot pocket cruiser cracked its centerboard trunk and I pounded my T-shirt into it with a hammer. We blew the nine-foot daggerboard out of a 36-foot racing trimaran at 15 knots (sailed over a submerged jetty), and that took several T-shirts and most of the cabin table to staunch. We lost an outboard rudder off Bermuda which left holes in the transom, and I crawled into the stream and pounded cushion foam into the holes. Sure we carry wooden plugs next to each thoroughull, but they're not always the solution.
If a dripless shaft seal bursts, it is necessary to immediately wrap the leak with something, anything, get it under control. It helps to consider in advance how to do that, but even if a total surprise the need is for immediate aggressive action with whatever's available.
The accident boat above made a Mayday call before the source of the leak was discovered.
Find the leak first.