The quickest way to identify good links is by setting the filters in Monitor Backlinks. 

First, go to Backlinks > Filter:

Finding Good Links

To find good links, set the following filters:
 - Majestic Trust Flow higher than 10
 - Majestic Citation Flow higher than 10

After applying that filter, for each backlink check:
 - that the number of external links is under 100 (and under 25 is really good)
 - that the content on the backlinking page is high quality

If all of the 4 points identified look good, then it is most likely a good link. 

Finding Bad Links 

To find bad links, set the following filter:
 - all warnings

After applying that filter, go through the links and do a manual review. The biggest factor in identifying the quality of the link is the content of backlinking page. The content should be high quality, and ideally relevant to your own site. 

Having a warning definitely does not mean that it is a bad backlink. It is just a helpful indicator. 

Other Resources

The Ultimate Guide To Find Bad And Good Backlinks (a more detailed guide)
What Backlinks Should You Disavow
How To Analyze If It’s Worth Getting A Backlink From A Website
Check If Your SEO Company Is Helping or Killing Your Website

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