To remove a skill from your company, click on Skills in the left navigation menu. On the Skills page, locate the skill you wish to remove and click the orange wrench icon in the Edit column. Next, click on the red wastebasket icon.
There will be no confirmation to delete the skill but you will have a moment to undo the deletion.
Note: You are not able to remove a skill that is associated with a job (i.e., a requirement of the job).