Sure. I think being honest is a solid choice, generally speaking. There is some etiquette. If you're way too direct, you might be perceived as a creep. But you certainly have to do something, or it won't lead anywhere.

Telling people you want to stay in contact, or you think they're attractive, or you like their outfit, or whatever people do for flirting seems to be alright. Whatever floats your boat. I think the one important thing is to read the room. See if they're comfortable. And if they enjoy talking to you, or if you've just cornered them and are monologuing. Most (not all) people can do that. And I'd say as long as everyone is comfortable, it's the right thing. I mean you have to send some signals for them to know what's up with you. So yeah, that kind of directness might be helpful. And after that, spending time together (and not just in a larger group) is a signal, too, in my opinion.

I don't think there is any general, correct way of doing it. It just depends on the situation, on who you are, and especially what the other person likes.