So I have no problem approaching, and once I do I get in the mood and can get some pretty good game going, but if I'm introduced and I don't open the set, I get stuck.

For example, me and a couple buddies were invited to a female friends house last night, and there was a gorgeous girl there, but I froze up. I didn't get to open her, my friend was like, "Sparroww, this is HB, HB this is Sparroww, and I just went AFC and was like, Hey hows it going? and pretty much made no attempt at gaming her all night.
Also, I usually run direct game, and I feel weird running super direct game on a friend's friend right in front of her.

So, advice? Should I just work on my indirect game? Or is there more to it than that?

Well it all depends why your friend is introducing you.
If it's his sister/target/nience/friend or whatever it would be nice to ask for permission just to avoid the awkwardness and make sure he doesnt get in your way.

It kind of depends on style, I'm straight forward about my intentions, when a friend introduces me, I ask his with a grin on my face:
"Wow, she's awesome! Is it okay for me to hit on her?"
Possible responses: No, she's got a bf/ Nah I kinda like her/ Dude what the hell?

Or the girl just replies: I think can decide for myself:p

Just do it in a fun way. But if you don't you could always talk to her like you would talk to any other human being and possible game her later if you ask your friend for permission in private.

I personally try to conflict conflicts over stealing a girl from friends so my style would always be to try and ask for some sort of permission.

Just note that you just keep a light and fun SPAM, you don't want her to start avoid going to your friends how because that guy who asks me to have his babies was there;)

Cheers