First of all, I used search and there was nothing very precise, so I'll make a clearer thread.
How this works: You either gained a saddle from a dungeon, or you have created one by yourself. Note that the saddle is universal for any mount.
Creating one by your self is semi-costly It will require 8 iron , 2 string ]" title="-<->" /> , and 7 wool .
The stirrups will look like this:
 = stirrup
you will need two of these.
You will place all 7wool and 2 string on the crafting square, this will create a base.
]" title="-<->" /> ]" title="-<->" /> = base
You will then place everything like this to create a saddle:
  
  
And there you have a saddle.
Now to domesticate animals, you must approach an animal during a time when it will not attack you. You will go to an animal and feed it either :////:, , , or a depending on the type of animal. Ex. Spiders would eat meat.
You will feed them until they start following you, you can then place a saddle on them if you wish to ride them.
Domesticated animals will follow you, you can right click a domesticated animal to follow, stop, or graze/defend.
Domesticated animals will remain there forever, until its killed.
Some animals can't be domesticated, such as a dragon. If you want a dragon, you must hatch one out of an egg.