Dragon saddles are found in the chests of final rooms of dungeons. They let you ride on dragons, but you need to combine them with certain crafting materials in order to make them suitable for your dragon. Example: Water Dragons would need a Saddle with either Ice Blocks or Water Buckets around it to make a Wet Saddle. Air Dragons would need a Saddle with Wool Blocks around it and so on.
To craft any Dragon Saddle you must first need a Dragon Editing Table. (more information will be at Dragon Editing Table )