If they were out in public just walking around, I might casually approach them and tell them how much I appreciate their work or what they stand for, etc. But if they were at a restaurant or enjoying what should be private time with friends or family, I would leave them alone.
If you saw a famous celebrity who you see as an inspiration, how exactly would you go up and talk to them?
I was lucky enough to meet John Wayne when I was in Vietnam but he came up to us to meet us and talk to us. I got to shake his big hand and got an autograph. I couldn't say a whole lot as there were quite a few of us there and I was just in awe of seeing him up close and real. I can't think of any other actor I would like to talk to. I can think of a few actresses but the security around them would be strong and I highly doubt that they would let anyone close.
I am with Barb, if they are eating or with family and friends I would leave the alone. If I saw them out walking somewhere, I would approach them holding my hand out for a handshake, and say "Hello, Mr./Ms. ____, My name is ____ and I just want to say thank you for being and inspiration. "
I don't know that I would....no one inspires me enough to go up to a strange person and strike up a conversation....that's normally something I avoid.
I'm sorry to say I've not yet seen one that's an inspiration to me. So I wouldn't .:(
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I can't really think of a celebrity that inspired me after I became an adult.
Over a 50 year period, I have run across a number of them in various situations.
And there have been a number of them whom I have enjoyed in TV and / or the movies.
If they are alone and stationary, I will occasionally simply say that I have your enjoyed your work in "fill in the blank." That's my gambit, then things are up to them.
Same if they are eating, but I do not enter their personal space to offer a handshake (that's just me---I tried that once and the actor was was eating ribs---finger food. Last time for that. Now I curb my enthusiasm.)
And I won't go so far as to cross the street and catch up to them---I like it to flow a little more smoothly than that.
I'd casually say, "sup Danzel, long time no see", and leave him wondering who the heck I am.
No celebrity really inspires me that I can think of ... I am in a relationship with Lenny Kravitz though even though he doesn't know I exist... So when I meet him I'll just walk up to him and say " how youuuu doin ? ;) then he will fall madly in love with me cos he's totally into dilutional blondes. ;p