There are several telltale signs of a peer-reviewed article. (See the FAQ "What is peer review?")
When searching for peer reviewed journals from a database, select the "peer reviewed" or "peer reviewed & academic" filters in the database you are using to ensure that only journals that have a peer reviewed policy for at least one kind of article are returned.
Other factors to look for if peer review status is not obvious for the article itself:
If the article has the actual phrase “peer reviewed” or “refereed” on it.
If the article (on its first or last page usually) has a listing of dates of (peer) review such as: submitted, reviewed, accepted, published, etc.
If the article is described as an original article, full article, research, etc.
Pretend you’re the author of that article and go to the journal’s website to look for “requirements for authors.” In this section, you should be able to find what categories of articles get reviewed for that particular journal.
You can also use Ulrich's Web to find out if a journal title is peer-reviewed, in addition to the above clues about a particular article in the journal.