Some of the criteria may have already been covered in eliminating unwanted publications during your search. In other cases you apply such criteria to evaluate which literature is worth reading first. You choose the approach you are most comfortable with, given the search tool you use, or the approach that fits your study topic best. In the part How to evaluate your search results you will find more practical details on how to apply the quality check.
Two evaluation approaches are worth mentioning here.
CRAAP stands for Currency, Relevance, Authority, Accuracy and Purpose. The CRAAP Test was created by Sarah Blakeslee, of the University of California at Chico's Meriam Library. Several variations are available on internet. The test was designed for a multidisciplinary context. CRAAP can be used for websites, books, and articles. See The CRAAP test - Evaluating info and the handout The CRAAP Test Worksheet (PDF).
A practical application, using CRAAP for a quality check on websites, is offered by Bluford Library, North Carolina Agr. & Tech. State University:
By scoring each category on a scale from 1 to 10 (1 = worst, 10=best possible) you can give each site a grade on a 50 point scale for how high-quality it is!
The proposed scale is then: 45 - 50 Excellent | 40 - 44 Good | 35 - 39 Average | 30 - 34 Borderline Acceptable | Below 30 - Unacceptable
ASPECT is the acronym for Authority, Sources, Purpose, Evenness, Coverage and Timeliness. This checklist was developed by Clark College Libraries in Vancouver, WA.
Currency is here called Timeliness. Authority and Purpose are mentioned here as well. Evenness and Coverage in this approach compare to towards Accuracy and Relevance in CRAAP. See the research guide Evaluation information at Clark College Libraries for more details and the handout: The A.S.P.E.C.T. Checklist for Evaluating Information (PDF).