I work for a non-fiction book publisher and, believe it or not, we still have a few authors who index their books without a computer's help.
The process itself is not exactly different, just way more time consuming. Creating an index without digital aid happens just before it goes to the printer. The author most likely already has a list with all the index entries he deems necessary. In our case, he then gets a printout of the almost complete book, reads it front to end and whenever he stumbles upon something that is on his temporary list, he simply writes down the page number. After that we take his list, bring it into form and add his hand-written page numbers.
Now you might ask: why don't you help him? The problem, especially in historic non-fiction books (which we mainly publish), is that even with a search function, you can not reliably look up and link each index entry. A recent book we published quoted lots of medieval sources. Now the mayor we might nowadays know as "Hans Burckhard" will most likely not be referred to under that name. One source might put him as "hanns burghard", another as "burkhardt hansen" and so on. If multiple people have similar names, only the author can safely distinguish between them and no search function will match all mentions in the text.
I hope this can shed some light on the indexing process without computer help and is competent enough to be accepted by the mods. If I don't seem credible enough, I can provide proof that I indeed work in book publishing. Please excuse my simple English, too, I'm not a native speaker.