The unicorn can be found in Harcane's Grove, being protected by three minotaur lords. To ride the unicorn make sure no weapons are equiped or it will attack you. You must also make sure you do not have your fists out. Once you have done that you can run up along side the unicorn and ride it away.

Oblivion Unicorn's Statistics

The unicorn and the white horse have the same speed. However, the unicorn differs from the white horse because it is more powerful, and has certain special abilities. If you dismount off the unicorn it will always start to go back towards Harcane's Grove. So don't let it out of your sight too long or you may have to go to Harcane's grove to find your Unicorn. The Unicorn must be killed to complete Hircine's quest because you will need its horn. The Unicorn is not good around people or other animals. If a person or another animal is around it will attack it, no matter if it is your ally or not. So make sure you do not have any allies around while riding your unicorn in oblivion. Another thing to take into account is your unicorn will not attack you if you have very high fame and a very low infamy. So if you are trying to get an oblivion unicorn make sure you keep your fame high and infamy low.

Sources

I would like to thank oblivion unicorn for helping me write this page!