I hate to disagree with the above and normally would not, however I have worked for Google and because of that I feel I have an obligation to steer you right.
Penguin was mainly aimed at linkspamming so check the dates within analytics to be certain it was not a result of the Panda updates instead. If you have ascertained that it was definitely penguin then it's time to get down to work.
First I'm going to admonish you for linkspamming, it was always against Googles Webmaster Guidelines and you should never have done it in the first place. Any unnatural link (one you have built yourself or had a bot like xrumer build for you) is bad in the eyes of Google. We all make mistakes though and Google will forgive you if you rectify matters.
Google (who I'm now going to refer to as "it") gauges the value of the link to your site by looking at the anchor text. In the case of spamming, much of the anchor text is similar. Providing a link to an external site is a way of adding to their reputation and this is the basis of the algorythms used. In the case of ethical SEO, the site links to you because it likes your content, in practise, this comes in many ways, differing anchor text, linking to subpages, nofollow & dofollow links, different positions and text. Because of this, linkspamming is easy to spot. Your site should not have de-indexed you so if you check site:domain.com on Google all your pages should still appear. But what it did do was to reduce the value of the incoming links.
Use Google to find all your links (or if there are more than a few thousand, use Open Site Explorer) and check the anchor text, If you're getting over 10% of a certain anchor text then you're going to need to do what you can to delete that link.
Once your existing links are cleaned, then you can start to go about building some ethical links (press releases, guest blogs etc, some links associated with relevant content).