I used to flush PS systems by removing the return hose and then pouring parts washer solvent into it while the engine is running. Then the EPA took away my parts washer.
It is best to flush the system with either the correct fluid or a solvent that is safe for the system. If you are lucky to use ATF, just unhook the return hose, have an assistant fire up the engine and pour in several quarts of ATF. be careful, it comes out hard and makes a mess. Stick the end of the return hose inside of a big piece of heater hose and route it to a big pan on the floor.
If you use the mineral oil stuff, I don't have anything responsible to recomend aside from running $20.00 a quart oil through. It is safe to run the system dry for a brief moment. So you can remove the return hose and have someone start the car and shut it off instantly when you scream at them to shut the car off when it runs dry.
If the wrong fluid was used, most of the damage is already done. the best you can hope for is to get the bulk of the contaminates out and hope for the best.
If your system uses the mineral oil, don't put any kind of additive or conditioner in that does not clearly state its safe for it.