Your contact's Overview screen contains a Keywords section for the contact. Below is an example of this section:
Clicking Edit in the top right corner of this section will allow you to select new Keywords to add to a contact (or to delete existing Keywords from their record).
Also, if you hover over a Keyword in this section, you'll see a minus (-) icon that will allow you to remove the Keyword from their record:
You can learn more about working with Keywords here.