How do I enhance my skills?

As it states on the skills page on the Wikihack: you must still have a number of successful uses of the skill before you can enhance it.

The number of uses is below (again from Wikihack)

Skill Level  - Successful Uses
Unskilled    - 0
Basic        - 20
Skilled      - 80
Expert       - 180
Master       - 320
Grand Master - 500 

_{Note that successful uses are total, so to get to the next level subtract the destination level from the current level.}

For example if you are Basic in Dagger you must attack with a dagger successfully 60 times (80-20) before you can raise it to Skilled.

You also must have a free skill slot, obtained by leveling up.