Within the TV series, it's pretty clear that Amanda Grayson's attraction for Sarek is in no small part led by her overall admiration for Vulcan culture;
AMANDA: You don't understand the Vulcan way, Captain. It's logical. It's a better way than ours. But it's not easy. It has
kept Spock and Sarek from speaking as father and son for eighteen
On top of that, it's obvious that despite the Vulcan aim to hide their emotions behind a façade of logic, that she is very well aware of his affection for her, something he finally admits in his failing years suffering from Bendii syndrome;
Sarek : Amanda... I could have given you so much more. I wanted to show you
tenderness. But it is not our way. Spock...Amanda did you know?
As to how they met, there's a brief mention in one of the TOS episodes that Amanda was a teacher. In the (non-canon) Vulcan Academy Murders book, it's revealed that she was teaching at the Vulcan Science Academy on Earth, tasked with educating recent Vulcan arrivals about Earth culture. The Academy was part of the Vulcan embassy and as Ambassador his duties included teaching and lecturing. Because of this, they were both in regular contact with and ultimately ended up marrying after a brief courtship.
As System Down mentioned in his comment below; the non-canon book "Spock's World" also has a slightly different story about how they met - I've edited it for brevity;
Quite shortly thereafter, he met Amanda Greyson.
It was, of course, in the line of business. She was involved with a
Federation program intended to develop a universal translator, and
Sarek was happy to have his linguistics department assist her such an
instrument could only be a tremendous breakthrough, in a world where
until now wars might be caused or averted by the mistranslation of a
term. She did not make any particular impression on him when he saw
her first-a handsome woman, tall for her people, with wise eyes.
Later, he found that she reminded him of TPau, in some odd fashion,
though he had trouble identifying exactly what the likeness was.
They met fairly often after that. Sareks Anglish was more flexible and
idiomatic than any of his staffs that was the excuse. But increasingly
he found himself delighting in having a friend. He had had few, on
Vulcan from a very young age, his work had possessed him. During his
earlier posting here, he had been on the move all the time, even when
working-gathering data, rarely staying mentally in the same place for
very long. But now, in his early maturity, he felt a little more
settled, and that settlement found great satisfaction in the
expression of friendship.
There came a time when the day seemed somehow incomplete if she had
not called him and asked him about something, or told him what she was