The easiest way to find peer-reviewed sources is by using the library's @LL Search to help filter your results. By choosing the Advanced Search option, you are given the opportunity to pre-select any filters; to limit your results to peer-reviewed sources, click on the Peer Reviewed Journals box within Search Options, as indicated in the screenshot below.
You can also use limiters after a search has already been made. On the left-hand side of your search results page, you will find a number of options for refining your results. By clicking on the Peer Reviewed Journals box, you eliminate all results that are not found within such journals, as indicated in the screenshot below:
Other academic databases will often have similar options for limiting. Just note that it may not be in the same layout as Lesley's, so you may have to do some investigating.
To determine if a source you found is peer-reviewed, have a look at this page for some tips.