Some have saved up, some have put it on multiple credit cards, some have gotten loans, borrowed from supportive family. There have been internet and IRL fundraisers.....just about anything.
There is also a thing called "Care Credit", but my understanding is the interest rate can be CRAZY.
It seems that many investigate and choose a surgeon first, so they have an idea of the needed amount. (Surgery/travel/post-op care). Perhaps your surgeon can accept at least partial payment from your insurance (depending on where you live etc). Perhaps they want it all up front. Perhaps they will or perhaps they won't accept Care Credit. Perhaps they will or won't split the amount between five relatives and three credit cards.