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You can get a horse to ride by talking with the caravan at Riverbank. After that he will give you one horse (you can should your own horse), and after you build a stable. A horse you chosen will be right there in you stable.

After you have a stable, you can catch some rideable monster like woubulk, rapter to ride.

If you're refering to being unable to teach it "mount" as a command, just feed it a bunch. 

To teach your animals commands  you need to have a certain like with them. Usually around 10-15 unlocks all commands