Here is a suggested set of questions to ask yourself when making an assessment of any published source of information, not just websites:
Who authored it, and what are his/her/their credentials? In the case of a book, there may be something in the 'blurb' on the back cover about the author. In academic publications there are often notes about the author(s) and their qualifications and experience which enable them to speak authoritatively about their subject. Are they affiliated to a university or a research institute?
Websites are often created by more than one person, but it is still important to check who the authors are. See if there is an 'About Us' link giving information about the website, or the organisation and people maintaining it. Are there any reliable contact details? What are the stated aims of the organisation?
Does the book or website contain up-to-date references to source materials, particularly to original research or statistics, so that you can check whether the discussion or opinions are based on reliable facts? Is it aimed at a popular audience, or is it more scholarly and reasoned in its approach? What kind of language does it use: is it rhetorical or emotive, and does the author back up his/her/their arguments with appropriate facts and original sources?
Think about the possibility of any bias in the information you have found. Is it possible that the organisation represented by the author or website has a particular standpoint to promote: is it a campaigning or pressure group, a government department, or public information service?
If the source is likely to have a bias, make sure you check any references or links provided, and find some other sources with a contrasting standpoint, preferably from an academic book or journal. It is good practice to use a variety of sources of information so you can compare and contrast different viewpoints on a topic.
Check how up-to-date the information is. A book or a journal will usually have a clear date of publication on its cover or title page. If it doesn't, check the date of the latest item in any bibliography at the end of the book or article.
In the case of a website, try to find the date when it was last updated. In some subjects such as law or economics, the validity of information may change more rapidly than in others, so you will need to be careful. Are any links from it to other sites still active?