Google released their new disavow links tool with a load of cautionary tape around it. In this 10 minute video Google's head of web-spam, Matt Cutts, gives an overview of the new tool and the precautionary tape around using it.
Google gives a few big things to consider before using this tool.
The majority of websites will never need this tool
If you are the average website owner, you follow good guidelines or a simple mom-and-pop shop, there's a good chance that you will not need this tool. This tool will only be used by those who participate in SEO efforts and have spammy link profiles that they would like to clean up.
Clean up as many links as possible directly with the website first
Google always recommends to work directly with the website to get all the spammy links taken down before using this tool. They suggest only using this tool as a last resort if you cannot get a hold of the website or cannot get it taken down.
Take your time, do research and be cautious when using this tool
You must really take your time to use this tool correctly, if you don't, you may be doing more harm than good. Use Google webmaster and Open Site Explorer to download your inbound links and carefully research all the spammy links.
Be cautious when adding them to your .txt file you're submitting to the disavow link tool because once they are submitted they will be MUCH harder and take MUCH more time to get changed back, if even possible.
If you have watched the Matt Cutt's video and followed the above considerations, then you can decide if this tool is right for you. If you decide to use it, you can access the tool via the Disavow Links Page in your Google webmaster account where you can upload the .txt file of links you'd like Google to disavow.
Keep in mind, this is simply a highly weighted suggestion to Google and they still reserve the right to make changes or deny any requests. Additionally, it can take 2-3 weeks for your changes to take effect because Google must go back and re-crawl those linking pages to add in the correct link attribute to disavow that link.
This is a new and tricky tool. If you have any questions, feel free to post in the comments for help.