The first place to start the cleaning process is the conchos. I have marked them in blue in the picture to the right. I like to remove the conchos so I can get up under the overlapped leather. Most people never do this when cleaning.
To remove a concho you must first undo the saddle strings. You can see in the removing concho picture with a blue arrow that there is a slit in each saddle string. The strings are woven through these slits one on-top of the other. If this is an old saddle or brittle strings they could break. First moisten them with a spray bottle of water. Then slowly pull the strings through the slits. I sometimes use a small pair of needle nose pliers, especially if I plan on replacing the strings during the restoration process.
Once the strings are loose the concho can be removed. On this saddle there are leather conchos under the metal one. There is also a nail you can not see in the picture in the middle of the 2 leather conchos. That must be pulled to loosen up the saddle. This is the first time your screwdriver and nippers will be used.
Under the leather concho there was another nail through the jockey. Each concho I removed was exactly the same way.
NOTE: Removing nails can be difficult. Most of the time they are old and rusted. I normally pry with the screwdriver first to break it loose. Then I use the nippers to pull the nail.
WARNING: Removing nails is tricky business. It is easy to damage the leather or open the nail hole up, possibly destroying the leather. Take your time and treat the saddle as a priceless possession.