There are a wide variety of ways that instrument producers make their measurement tools available for use and/or adaptation. Permissions and whether or not there are fees to use an instrument are discussed in records in APA PsycTESTS (there are also search limits for these features) and Mental Measurements and Tests in Print.
Terminology varies across databases and sites, for example, the National Center for Interprofessional Practice and Education uses four Access categories which are not mutually exclusive. Their categories listed below may not be used in the same way as on other sites--for example, although only one is called Copyrighted, it is likely that all of the instruments with the exception of those provided by the federal government have rightsholders. Open access instruments may have an associated license, such as a Creative Commons license.
If you need to seek permission or an exemption to use the instrument, visit the UC Office of the President Copyright and Fair Use Pages.
The search approaches in the sections of the guide above include how to search the Measurement Instrument Databases and Literature Databases by language. However, there will be times that no instrument is accessible in the languages read by the population you wish to have participate.
Considering developing your own instrument? The UC Davis Library has helpful background reading, such as:
Two options at UC Davis for securely deploying an instrument online are REDCap and Qualtrics: