Defining what good evidence is can be difficult - it depends on your research question, academic discipline, and other factors.
At the Masters level, "good evidence" is generally considered to be peer-reviewed research. Peer-reviewed research has been submitted to a publisher and then read by other scholars in the same field who review the content to make sure the researchers methods are sound and their results seem plausible. Often they submit feedback, including suggestions to include more citations to relevent work they may have missed, so that the paper can become stronger before publication. They also have the ability to reject a paper for publication. In this way researchers have the understanding that what they read in a journal is well-researched, verified, tested, and based on sound methodologies.
If you are interested in learning more, check this video by the North Carolina State University libraries.
Google "Speech Therapy Research" and you will get 4.3 million results, most of which are not going to be research articles. This is why you want to start your research in a scholarly database.
You may notice that some of the results only have abstracts and others have full PDFs. Some times you'll get to a publishers webpage that will ask you to purchase the article. Don't do this! Never pay for articles. The MSU library can almost always procure articles for you at no cost. You can contact librarians in many ways, including chat reference. As a graduate student, you can also use MARS, the MSU document delivery service which will scan and deliver electronic copies of print journals and book chapters.
An introductory video to evaluating sources is found below:
If you ever have questions about a source you have found, feel free to contact your subject librarian for a second opinion.
If you can't find something through the MSU catalog or webpage check out Inter Library Loan (ILL). They can help you find resources you thought we didn't have and request materials we don't have from other institutions. This service is always free and often you can receive materials as a PDF.