Diagnosing Penguin and Panda penalty
As a website owner or marketer, you may be asking yourself, "How do I know if I've been penalized?" Beyond the obvious answer, "check your sales receipts," there are options. The first and best indicator that you've been penalized is based on whether or not you received this warning message via Webmaster Tools:

If you are one of the lucky recipients of this message, I suggest skipping ahead to the next section. If your sales haven't been significantly impacted and you haven't received a warning notice as far as you know, then the next step is to review your analytics. Look for dips in traffic associated with the timing of the updates outlined in the timeline above. Below are two examples of websites hit by Panda and Penguin updates:

Once you've confirmed that you've been hit by Panda or Penguin updates, the next step is to determine why you've been penalized. The best way to do this is to conduct a detailed forensic SEO audit of your website and overall presence. Pulling from the "3 Cs" methodology, evaluate your content (freshness, quality, relevance, and originality), code (clean, unstuffed with keywords), and credibility (quality links). There are a variety of tools you can use to evaluate your website and identify problem areas. I'm going to highlight two that I feel are relatively easy to use and affordable.
Tool: ahrefs

Tool: Open Site Explorer

Both tools provide insights into the link profile of your website, which is the most common violation. With both tools, look at the quality and quantity of your inbound links. Specifically, look at the "authority" of the inbound link, domain type (.com, .net, etc.), and anchor text. Google likes to see a natural or organic link profile, which includes a relatively even distribution of link sources, depth of inbound links into pages on your site, and variety of anchor text across those links. There are a host of other tools and elements to evaluate, but I have a day job, so I'll be moving on now. Feel free to read up on other diagnosis tools and techniques on reputable websites like SEOmoz, SearchEngineLand, and SEORoundtable.