I second the thought of learning something extra about the band/band member you're hoping to meet. For example, I have Stefan Elmgren's Full Strike CD, which Bjorn from Freak Kitchen was on. I of course, had him sign it, which got a very amused "WHERE THE FUCK DID YOU FIND THIS???" out of him. So then we (briefly) chatted about his drum style on that album, as compared to his drumming with Freak Kitchen.
I also asked Christer from FK about his horse tattoo, since I really like horses. He seemed somewhat suprised that I was asking him about his tattoo, but he seemed pretty happy to tell me all about it, anyway. And then I realized I was holding up the signing line, and tried to thank him and move on. Upon shaking my hand he noticed that it was very cold, grabbed it in BOTH of his hands and said "Your hands are cold!" To which we had a very brief discussion about that (I was worried about pissing people off in the line behind me) and it ended with him saying "But your heart is warm."
I'm still not sure what that was all about, but the FK guys are my favorite people just because they were all very nice. Mattias chatted briefly with me outside of the venue and gave me a hug. He remembered me from the signing.
I (and two friends) ended up chatting for a good long time with Daniel from Sabaton, too, simply because my friend Mallory (the girl with the cutlass tattoos) absolutely LOVES Sabaton, and was terrified to say hi. So I went over to him and told him how my friend loves his band, but was too nervous to say hi, while dagny_t basically grabbed her and flung her at Daniel. Hee! Poor Mallory! But for much of the fest, we all hung around and chatted with Daniel. He was very sweet, and introduced Mallory to other members of the band, if they came by. He even told us some off-color jokes.
Mallory ended up getting to hang out with Sabaton later on at the hotel, and they all took pictures with her, and gave her a t-shirt. She was absolutely over the moon when she got back to the hotel she was sharing with me and my friends.
dagny_t and I also pretty much pounced on DSO after their set. dagny_t found out that Anders, the bassist, has been to Colorado for awhile, which is where she's originally from, so they had some common ground there. She also chatted a bit with Annalouice about singing, and she gave Daniel, the other vocalist/guitar player a neck rub, mostly because he said he was sore from the flight over and I gleefully said "Oh, Jessica gives GREAT massages!" Mwahahahaha... I think we might have embarrassed the poor guy, but he was very gracious about our fangirling.
So it helps if you have friends who are pretty much fearless, and will force you to say hello to a musician you like, but it's even better if you muster up the courage to say hello for yourself. Most musicians seem to like it if you know about other projects they've been doing, or ask them about something that may be personal to them, like if they have tattoos, or something similar. And often times, they just seem to like hearing "I really like your music." Sometimes, the best thing you can do is just to let it show that you truly love what the band/musician is doing.