The standard format in the UK for an introduction is usually considered something like:

    1 : have you two met?
    (2, 3 indicate no)
    1 to 2 : this is 3, she's a number too
    1 to 3 : this is 2, he's prime

I guess it depends on local factors.

Same here. But if I have forgotten a name or failed to recognize somebody who obviously recognizes me, I'll do the first step and hopefully the second step, and then pause. From there, people self-introduce (something they do all the time if there's nobody to introduce them).

You try to aim for an informal introduction. Get two people close together, nudge them towards each other, say the "have you two ever met?" line, and just leave it to them to exchange greetings.