My tips:

• Read primary sources (e.g. the bill itself, the court document itself, the mueller report itself). If news outlet X broke the story, read their version of the story because often second hand reports add/remove things.
• Bias is inevitable, but it can be cancelled out if you don't just stick to one source or to many sources with the same bias.
• Bad/false sources can still be useful to read because they give you a perspective on what the (perhaps large) portion of the electorate who believes that source is thinking.
• Read with a grain of salt the sources that use emotional language (e.g. ripped, destroyed, gutted).
• For commentary try to focus on relevant professionals (e.g. lawyers/judges talking about law).
• Different sources will be better equipped to cover different subject areas.
• Bias isn't just left/right. It's also sensationalist or fact-reporting. It's also pro-capitalism or not. It's also US-centric or global. It's also layman or expert.

That said, whenever there is a megathread in /r/politics with like 100 article links, I'll usually start with Reuters, The Hill or Associated Press and then read others for balance.

Forgive placing them all in the same bucket, but some sources I've learned to read with skepticism are Fox, Breitbart, Reason, CommonDreams.org, Quartz, Buzzfeed, Vox, Huffington Post, Electronic Frontier Foundation and probably many more. That doesn't mean that I don't look at these though. They can raise interesting points and novel facts, I just read them with the understanding that they are more likely to say one side or to exaggerate/assume in favor of that side.