Site settings determine whether votes, likes or both are enabled:
Vote up / down
Like / Dislike
These effects are available just for the author of the comment. You can't vote up/down or like/dislike your own comment.
In case the site administrator set these effects to cost extra points (look at "Opportunities for Expression" in the "Help" tab in the widget), the buy-points dialog will appear.
But in case the effect is free it will be applied by a simple click on the corresponding icon.
Note: You can vote up/down and like/dislike other comments, but you may do so just ONCE per comment. These effects are permanent and you can't cancel it.