There are times in life when you may want to connect with somebody more "famous" than you. I mean famous relatively speaking. It could be a blogger, business person, government official, or even maybe just the hot girl/guy you see regularly at your local coffee shop.
The first thing you have to remember when you want to connect with anybody you admire is that we're all human. You, me, and that person you want to connect with. Huge revelation, huh? ;) Lesson #1: treat people like people, not like gods.
Whether you believe it or not, everybody is your peer. Don't act like a fanboy. Praise is OK, but don't fawn/obsess. It's weird, it's creepy, and it won't get you anywhere. (Except the brush off.)
I can't think of a single instance in my life where I've connected with someone by supplicating. Again, praise is OK, but don't go over the top. Treat people like friends. What would you say to a friend who wrote a great book or song or something of that sort?
"OMG! You are so awesome! You're the best! I love that book. What's your favorite color? Do you like cookies?! Want to hang out? Huh? Huh? Huh?"
Probably not. :)
If it was a friend you'd treat them normally. (I'm not saying you shouldn't tell your friends when they do something you think is awesome. I'm saying you're not going to go over the top and make them feel weird because you see them as peers.)
If you're trying to connect with somebody who is a "superstar" in your field don't take up too much of their time. Better to end the conversation first than to make them antsy wanting to leave. Make the first contact briefly, and follow up again later (via e-mail/phone or maybe later in person). If they ask you to sit down and chat or ask you to lunch that's another story. Obviously in that situation you can take up more of their time. :)
A small example: I think Leo Babauta is amazing and I'm a huge fan of his work. But I don't treat him like he's anything other than another guy. It makes it weird for people when you treat them differently.
Just be cool and you'll connect with the people you're supposed to connect with. You might not connect with everybody, but at least you won't creep everybody out either. :)