In the Fan section of the Configure Site > Social Networking page, you can choose to allow members to fan other members.  Like other features, you can choose the button images to fan/unfan a member, and how to display the fan/unfan image/text button.  

As a spamming control measure, here you can also set up the maximum speed of adding fans/seconds.  If over the fanning speed limit, the member will receive the message to wait, the language which you can specify and customize here.

If you use the Fan feature, the fan button and member fans/fanned will display on the Public Profile page of a member automatically, if you are using the Default page type format, and the website visitor viewing the page is a logged in member, and not blocked by the member.  On their Edit Profile page, each member can view members they have fanned and remove themselves as a fan if they would like on this page as well as the member's Public Profile page.

Also, if you are using the Page Commenting & Rating feature, when a member posts a comment, the number of Fans they have will be listed under their username/profile picture.