If your bathroom floods due to a backed-up toilet or any other issue, you need to turn the water off using the valve leading to the offending fixture or your home's main water valve. Then, you need to call an emergency plumber to fix the issue for you. While waiting for water damage remediation services, you can start assessing the extent of damage by checking the following three areas:
Under porous flooring
An overflowing toilet can put a lot of water on your floor, and even if you have mopped it all off the surface of your bathroom floor, keep in mind that the water can get underneath porous flooring. If you have linoleum that isn't appropriately caulked, pull up a portion of the flooring and feel if the floorboards underneath seem wet.
If your vinyl flooring is well-sealed and caulked, you likely don't have to worry about this issue unless you are afraid the water has seeped past the baseboards. In that case, remove a baseboard and check for moisture underneath it.
If you have a carpet, you can use a wet vac to remove as much water as possible, but you should also check under the carpet to see how wet the carpet pad is. If it still feels sodden after you have removed most of the water in the bathroom, remove it so that the water doesn't leach from the pad into other parts of your home, such as the room below.
If your flooded bathroom is on the first floor or the ground floor over a finished basement, you need to check the ceiling under the bathroom. Look for bowing plaster, water stains or drips, and if you see any of these signs of water damage, drill a small hole in the ceiling. If water rushes out, you may need to contact a water damage repair expert in addition to a plumber.
If a burst pipe caused your bathroom flood, you need to look at the wall behind that fixture or the wall around the pipes. Gypsum board mixed with water can mildew quickly, and once the fungi start to grow they can spread rapidly. If you have an access panel, open it and feel around for moisture. If there is no access panel, cut a small hole in the wall. If you detect water, consider cutting out the wet pieces of gypsum board and replacing them later, or have a waterproofing contractor do the replacement. By removing the wetness as soon as possible, you help stem the problem.