The unarmed skill is an innate skill; all classes knows it from the start, hence you do not need to visit a Weapon Trainer to learn it.
The unarmed skill is a requirement for wielding and using Fist Weapons (such as the Dagger skill is a requirement for daggers).

If you hit a foe whilst..

a) Being disarmed.
b) Having no weapons equipped.
c) Having Fist Weapons equipped.

.. you will be using your unarmed skill - hitting things with your fists.

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