Edit: the 1000s figure is not an exaggeration. Go to fiverr and search on "back link" to see.
- Download your links from webmaster tools.
- Edit the file so it contains just the undesirable links.
- Use the disavow tool [1] to upload the file. (If your livelihood depends a lot on organic traffic, that is one scary red button. The wording on the page coupled with the button text makes it sound like you will disavow all the links to your website.)
[0] http://support.google.com/webmasters/bin/answer.py?hl=en&...
[1] https://www.google.com/webmasters/tools/disavow-links-main?p...
"- Edit the file so it contains just the undesirable links."
That's the part where intensive manual labor comes in, weeding through those links one by one.
I also noticed that the help page states "(the file type must be .txt and it must be encoded in UTF-8 or 7-bit ASCII)". How many non-technical people even know what that means?
And what are the chances that if somebody doesn't know what that means they will mess it up? It is not like UTF-8/ASCII is something that you have to go out of your way to choose.. it is going to be what is defaulted to.