I work in a position that involves indexing and digitizing scientific literature. A major concept here is Optical Character Recognition or OCR for short. The page of the document is scanned and this software will transfer the image into actual text (remember, a scanned picture is just a picture - teasing out the characters to be able to compact things into smaller files is important). If the document is something hefty like a book, we can remove the binding and covers and the stack of pages (called leaves) can be inserted into a scanner for automated OCR. The process does produce errors, so someone like me will then look at the data (XML files) and fix errors manually. This more frequently occurs in highly technical literature with lots of equations and foreign characters. Something like a novel using only the English alphabet will be reproduced with relatively few errors.

OCR is one way. Another way, especially with older books or ones where the actual copy is of interest, is to use an overhead scanner. These usually use a camera to essentially photograph each page at a high resolution. The photograph is then taken, color-corrected, and entered into a database as needed.

To add to the excellent responses already in the thread, it is unlikely that a librarian does much digitization work directly. A librarian in a university library or preservation department is a professional position requiring at least a master's degree (some have PhDs). More likely a librarian will supervise student workers or para-professional techs who have been trained in equipment use and materials handling.

I used to be a graduate assistant in the preservation department at a major university library in the United States, and I used to have to do preservation photocopying, which is similar to book scanning in many ways. It's really mind-numbing, and there's no way any of the trained librarians in the department were going to do that. Their time is too valuable.

For Google or other e-book companies, I don't know what their corporate structure is. I do know that in my current university, which is one of the major contributors to Google's library, that I had one very annoying summer when Google workers were in the library pulling books and ignoring normal library etiquette about talking, eating, and playing music. I didn't ask any of them, but I think they were mostly local community college students and high school graduates. These guys were just pulling the books from a list of call numbers, though. I don't know who was doing the scanning.