Do a link audit of the site to determine the quality of the links and identify the bad links. There are several tools available on the Internet that can assist users in this exercise Some of these are paid tools while the others are free. For starters Google Webmaster Tools provide an excellent insight in this direction.

For such webmasters use the Google disavow tool by submitting the list of such domains to Google and requesting Google to disavow them. This list must be accompanied with evidence. that proves that you have made genuine efforts in contacting the webmasters of such sites and despite your requests they have not removed their links and so you want to disavow them.

Create a spreadsheet where the bad links can be listed and work can be initiated on them. Work will involve listing down the links and the date on which a request was sent to the owner of those links for removal , when a 1st reminder was sent for the same purpose; when was it followed up by second or third reminders and the status of the link currently - whether it has been removed.

It is important to properly analyze the reasons leading to the penalty and not to rush into submitting the site again for Google reconsideration.