There are tons of articles available on this topic, However I have tried to make this concise and give you only the information you need. The below 4 poitns will give you tips to create a Google friendly website after recent Panda and Penguin updates.

1. First let’s here directly from the horse’s mouth which is Google to see what they have to see on making Google friendly website  http://support.google.com/webmasters/bin/answer.py?hl=en&answer=40349

Here on this page, I more like the Things to avoid section which says,

• Don’t feel obligated to purchase SEO service , as it may be false claims
• Don’t use images to display important section of your website
• Don’t create multiple copies of page under different URL.
• Don’t fill your page with list of keywords

2. I especially like the tips given in the discussion thread http://www.go4expert.com/forums/showthread.php?t=532  … Some extract.

• Insert keywords at right place on your meta tags.
  2) Name your Images with Descriptive Titles and alt text.
  3) Use relevant text on your website.
  4) Use Ad sense to assess overall content relevance.
  5) Optimize Your Title and Meta tags.
  6) Use anchor text keywords in links.
  7) Submit your website to search engines and directories.
  8) Content updates
  9) Internal Linking Structure
  10) Link Building { One Way , Two Way and three way }
  11) Article Posting
  12) Press Releases
  13) Forums Postings
  14) Advertising
  15) Google Site map Creation and setup
  16) Blogs creation
  17) Make some videos and submit them to the larger video sharing sites like Youtube.
  18) Take part in social bookmark sites. These can get some good quick traffic (don't spam).
  19) Pay for direct advertising on sites that are on the same subject as yours.
  20) Take part in PPC advertising including Google Adwords, Yahoo Search Marketing and Microsoft adcenter and etc..
  21) Make an affiliate program for your website
  22) Do viral marketing by producing something with your sites link attached.
  23) Include your sites link in the signature of any emails that you send to people.
  24) Produce some business cards and get them distributed.
  25) Mention your website to your friends and family and ask them to pass it on to others (Word of mouth advertising).

3. Check out this article for deeper understanding on what works with Google  Real Google Friendly Website in 2012
4. Check this article (Creating a Google Friendly Website) which covers the basic things