Some general principles.
1. Recognize the difference between opinion and fact. The New York Times has both factual reporting--news stories--that is supposed to be devoid of opinion, and opinion pieces. Of course opinion and bias does creep into news stories written by even the very best journalist, and opinion pieces are usually full of plenty of reliable facts.
2. Corroborate. Find a second or third source to confirm facts. Better yet, if the same fact appears in a liberal and conservative site it's more likely to be accurate.
3. Know the source. Sam Wineburg talks about vertical vs. horizontal assessments of websites. Did you find the perfect article on a web site that you've never heard of? To assess its validity, reliability, bias, don't just scroll down (vertical investigation). Leave the site. Do a horizontal investigation of the site. Search the name of the site and/or its host on Google. The first place you will likely end up is on a Wikipedia entry on the site. That will probably tell you a lot. All Sides rates a lot of mainstream publications on a five point scale from liberal to conservative. Source Watch is considered to have a liberal slant by conservatives, but offers generally accurate ideological profiles of think tanks and also has sections on corporate PR and the conservative American Legislative Exchange Council (ALEC). See my Current Events Guide for a list of sources from different ideological orientations.
4. Wikipedia: Look under the hood. Click on the "talk" tab on the upper left of every page and authors' discussions about the topic. See what Wikipedia itself says about citing it as a source in a formal paper.
5. Seek opposing views. It is relatively easy to find different opinions. Type a topic into Google search bar and the name of a conservative or liberal publication.
6. Use fact check sites. They are pretty reliable and you can find a list of them on my current events guide.
Further readings on how to effectively search the web.
12 Ways to be More Search Savy. Some pretty nifty tips to Googling. https://ww2.kqed.org/mindshift/2011/12/27/12-ways-to-be-more-search-savvy/
Google has an online course called Search Education Online: http://www.powersearchingwithgoogle.com/
Google's tips for refining web searches: https://support.google.com/websearch/answer/2466433?hl=en&visit_id=1-636406894358693496-1803840044&rd=1
Looking for a now defunct website? Visit the Way Back Machine: https://archive.org/web/
Web country codes on the internet: https://goes.gsfc.nasa.gov/text/web_country_codes.html
About Wikipedia: https://en.wikipedia.org/wiki/Wikipedia:About
This is a fascinating behind-the-scenes story of a liberal purveyor of fake news. http://edition.pagesuite.com/popovers/article_popover.aspx?guid=e13d1154-2ffb-4306-83c2-9b5a0b094d13