Here is one account. I never considered myself a Buckleyite conservative but as a kid I was much taken by his show Firing Line. It is the first time I was exposed to Hayek (I recall that Buckley blew apart his critique of social justice with a single question), or for that matter Milton Friedman, or for that matter Johann Sebastian Bach. Here are many obituaries. Here is lots of YouTube, recommended.
Addendum: Here is Ilya Somin on Buckley.