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Make your landing page. This is the first page that people see when they type in your site's URL (www.yoursite.com.). Make sure that you have a headline, a picture of your celebrity on the front page, and a short write-up. Keep in mind that there are probably other fan sites for this celebrity. You should differentiate your site by explaining how your site is special, or what it offers that other sites don't.
Add interactive features. Fan sites are ideal places for like-minded people to congregate and socialize. You might want to include a forum for other fans to discuss latest happenings. At the very least, include your Twitter and Facebook/MySpace information.
Add multimedia. Maybe the subject of your fan site made some talk show appearances or was on the cover of a magazine. Maybe you have a rare early interview. All these things are of interest to fans and help make your site special.
Write a blog. This ensures your voice is part of the ongoing conversation about your fan site's subject. This also adds an editorial dimension to your site, making it relevant to current events. Most importantly, it gives your audience a good reason to keep returning.
Ask your site's visitors to share their own pictures, videos, comments and other media and text pertaining to your fan site. Publish these on your site as well.