If the tree is broken you will know it's broken!
Sometimes, you won't know. If you want to test for a broken tree, you grab the pommel and the very front and squeeze them together. If it gives, then most likely it is broken left to right. Then, hold the saddle by the front and back, straddle it, and squeeze with your legs. If it gives, it's broken from front to back. If it gives either way, have a saddle maker look at it. Other than that, the leather probably needs to be oiled. My leather saddle that I had squeaked like there was no tomorrow! Even after I oiled it. I ended up getting a wintec synthetic - no more squeaks!