This is pretty simple to achive really...
Goto your Ads and Pages area.
Click "Edit Page" under the page you wanna do this on
Click "Apps" on the left
Click "Add App" next to the Static FBML section
The custom FBML app is now added to your page. Now, on the same page under Static FBML click "Edit Settings" and make sure the Tab has "added" next to it (this means the tab is active and showing on your page)
Click okay to close that and then click "Go to App"
This is where the content of the page goes. The specific facebook tags to hide that stuff is <fb:visible-to-connection></fb:visible-to-connect>
As for the custom Like button..He is using an image and CSS..I think as long as you use the url points to http://www.facebook.com/plugins/like.php?href=http://www.URL-TO-YOUR-FACEBOOK-PAGE then when it's clicked the like will be added to your page/group/app.
So in the FBML section you can put
<b>Click the "Like" button To View More</b>
<a href="http://www.facebook.com/plugins/like.php?href=http://www.URL-TO-YOUR-FACEBOOK-PAGE"><img src="http://domain.com/image.jpg" border="0" /></a><br />
<p>bla bla bla</p>
Boom. Now, when you click the tab on the page you will see the bold text..Once you click "like" you will see the bla bla bla text.
Hope this explains it all!