PsycTests database has a Permissions field for each record which clearly outlines what you can do with a specific test.
The Permissions field will state one of these:
May use for Research/Teaching
Contact Corresponding Author
Contact Publisher and Corresponding Author
If the field states May use for Research/Teaching you do not need to seek permission to use this test, provided you are only using the test for non-commercial (i.e. teaching and research) purposes. The cover sheet of the pdf test will include more permission information specific to the test.
A commercial test publisher can provide important information for your research design, such as licensing to use the test (often involves a fee), test manuals with instructions on properly administering the test, preview copies of the test, and any special licensing requirements.
Option #1: Check if the test is indexed in the Mental Measurements Yearbook (MMY) using this website. If yes, search by test name in the MMY-TIP database and look for the publisher contact information in the test record.
Option #2: For tests not reviewed in MMY, Google works well to locate the publisher. This is because it’s in the publisher’s commercial interest to make the purchasing options visible through a Google search.