So my website was hit with Penguin not too long ago. What would be the best routine to recovery? Remove the links, or build a lot of links to 'burry' the bad links?
Depends on your current link profile. If you already have high quality links, you should remove bad links. If you don't have high quality links, get those first and then focus on removing links if your rankings don't improve. If you don't have high quality links and you remove all low quality links, your website probably won't rank anyways which is why you should focus on "burying" links.
If your site hit by penguin then you definitely received message from google webmaster about links, so first remove bad links then, edit your tag, and start building quality links,
What if my site hasn't received a message from Webmaster Tools. It just no longer ranks for the terms.