Here are four suggestions to start cleaning up your site:

If you have links from too many unrelated sites, such as directories, either remove some or try to get more links from related sites. You should have links from related websites at the minimum at 20 percent of your overall links.

If you have too many keyword links coming in, then vary your keywords and mix your brand name and URL in the links. Have at least 20 percent of your keyword links be non-keyword or brand-based.

If you are doing sponsored links, be careful! Cancel or remove any links you have from footers. Remove any sponsored links that don’t include a text description next to it. Contextual links are much better, meaning it’s better to have links from within text content of a website. 

Make the above changes a few at a time and wait a few days to see if rankings come back, before proceeding. However, Penguin will only run periodically like Panda, so it could be weeks before any affected websites recover their rankings.

If you do your own SEO, then you probably have an idea of which links are low-quality and what you should do. However, if you are a newbie and don’t know how to analyze your backlinks, try SEOMoz or Majestic SEO. They both offer limited free analysis, but for a more detailed analysis or analyzing more than one website, you would need to get the premium version.