Notes: So, I know that River describes the 10th Doctor as an unfinished photo to someone else, but the analogy seemed appropriate, so humour me, yes?
It's not until he's much older, and looking into the eyes of a much younger River Song, that the Doctor realises exactly how she must have felt that first time he met her in the Library. Now she is the unfinished photograph, and he the one looking at it.
They haven't actually been introduced yet, but he knows it's River, partly because of the hair and everything else, but mostly because they've only been in the same place for five minutes and she's already kissed him.
Apparently, she's just finished her undergraduate degree, and the graduation ceremony is today. The Doctor's the first attractive man she's seen on campus, hence his being on the receiving end of a celebratory snog.
After all they've been through (from the Doctor's point of view), it feels more than a little strange receiving such a casual and meaningless kiss from this woman.
Of course, there has never been an occasion when everything has gone smoothly while the Doctor and River Song occupy the same bit of time and space, and this time is no different. River might not know it, but for her, this is the first of a long series of adventures.
The Doctor pulls her out of a pile of rubble after the alien ship collides with the graduation hall (such impeccable timing, these aliens), and then keeps her by his side for the rest of the ordeal, making sure she's safe.
When everything's over, he heads back to the TARDIS and is just about to step inside when River pulls him back and kisses him again. This one lasts a little longer than the last, and the Doctor has time to reach up and stroke her hair before she breaks away from him. She regards him warily, as though she can almost sense their history.
Looking over his shoulder at the TARDIS, she asks, "Who are you?"
He smiles mysteriously, and before disappearing inside, responds with a word that will make sense to River soon enough.