It sounds obvious, but broken glass can be very sharp and therefore dangerous. It must be handled with care.
When removing a broken or cracked pane of glass, wear thick protective gloves and always wear safety goggles to protect your eyes.
If the glass has been holed, gently lever the remaining pieces out, starting at the top. Large pieces of glass are heavy so have an assistant, also protected as above, to help you.
Cracked glass
If the glass is cracked, but no pieces are missing, you will have no way of grasping the glass to remove it. Use a glass cutter to cut around the pane an inch or so from the frame. Place adhesive tape over the cracks and tap the glass gently from inside to separate one piece at a time. The tape will help to prevent the pieces dropping out.
Preparing and cleaning the frame
Once the broken glass has been removed, use a hacking knife to cut away the old putty.
Keep your goggles on to protect your eyes.
Holding this knife at an acute angle to the frame, you should be able to tap it with a hammer and remove the putty without damaging the frame.
As you work along, you will encounter the small retaining pins or sprigs in wooden frames or spring clips in metal frames. These can be removed with pincers.
Use the hacking knife or an old blunt chisel to remove all the old backing putty as well. It is important to get back to the original frame so that the pane of glass will sit correctly in it. Dust out the frame rebate and apply a coat of wood or metal primer according to the frame type and allow to dry. Failure to prime the surface will lead to deterioration later.