AFAIK they use Anycast for the multihoming [0] - It follows the normal routing process, but the anycasted network is announced from multiple sites instead of just one.

AFAIK Google have ~19 data centres, and DNS / 8.8.8.8 is probably being served from all or most of them. So it is indeed very reliable.

[0] https://en.wikipedia.org/wiki/Anycast