How to get an automatic "like" in a fan page after login?

You can't. Facebook policies restrict you from requiring or automatically Like'ing content from your users. You can put a Like button on your website that points to your Fan page and say "Like us!". You can also use our Page Tab feature to implement a Reveal Page / Like gate on your Facebook Page tab which can reward user's for Likeing the page (with a coupon or something). However, that works on a Page Tab on your Facebook Fan Page, not on your website. A demo of the Page Tab / Reveal Page feature can be seen:
www.facebook.com/SourceCoast/app_140333712712019
You can see how that page was created from our demo site on the page below:
demo.sourcecoast.com/index.php?option=co...cle&id=14&Itemid=189

Hope that helps!
Alex