How can I make the fans to come & check out my brand-new club?

You can post links to it in a related club. For example, if it's a club for a particular character, you could link to it in the club for the TV programme/film/book the character's from, the club for the actor or actress etc. You could also possibly PM the link to some members whom you know might be interested in joining - but be careful with this idea, because some people would just see that as spamming.

Mainly, you just need to be patient. Building up club memberships seem to take ages. Most of the clubs I've made only have myself as a member still, and the rest have 3!