To increase rankings, what things should not be performed to avoid a penalty?

You can use Google Disavow tool to remove low quality and spammy links. After getting rid of all the bad quality links, you will create authentic and good quality links from white hat SEO techniques which are approved by Google Penguin and Panda like the*link from social media, forum posting, article submission, guest posting, and blog commenting.

First of all, you will have to follow each and every guideline of Google and need to do an ethical SEO. You should not be performed below black hat techniques to avoid a penalty:

1. Keyword Stuffing
2. Doorway pages
3. Hidden Text
4. Clocking
5. Duplicate content
6. Link exchange
7. Buying backlink
8. Irrelevant backlink