It is important to remember when it comes to broken stairs that not all stairs are the same. You will need to examine your individual stair situation in order to see if the instructions will work for your specific stair problems. However, if you keep reading you will find some general instructions as to how to fix broken stairs in order to make your stairs safer to climb.
Inspect the stairs. Most of the time it is possible to replace only one or two of the stair treads rather than replacing the entire staircase. This is good news because a complete reinstallation of stairs can be costly in both time and money. If the stringers (the actual framework for the stairs) are damaged beyond repair it may be necessary to seek professional assistance in order to meet code or ordinance requirements in addition to the safety aspects of hiring professionals. If the stringers are in good shape you may only need to repair broken stairs or treads and this is something you may be able to do on your own.
Remove the damaged stair (or tread) and any nails that may be left behind. Make a note of damage (if any) beneath the tread and repair what needs to be repaired before moving on. If the area beneath the tread is left damaged you are going to need to make the repair again all too soon. Fix the problems beneath the surface in order to insure that when you repair broken stairs the repairs will last.
Purchase finished treads that closely match your existing stairs and cut them down to size so that they will fit your stringers. A general rule of thumb for cutting anything is to measure twice so that you only need to cut once. If you are less experienced with this type of labour be sure to add another time just be sure.
Attach the new stair to your stringer with wood glue (assuming you are using wood), hammer, and nails and you have learnt to repair broken stairs.
Be cautious when walking on the new stair at first as it may be slick. There are stair tread covers and adhesives you can purchase for the sake of safety. Remember to always wear safety glasses and gloves when doing this type of work in order to protect your eyes and hands.