When you want to conduct a search using one or more Custom Metadata Fields, simply go to Assets / Custom Metadata.
If you are an admin, you will see the familiar modal that you use to create your custom metadata fields, but now you will also see checkboxes next to each of the fields. You can check one or multiple boxes and then click the green Search button to see the results.
For those users who do not have permission to create custom metadata fields, they will still be able to access this modal and use its search functionality, but they will not be given the option to add/edit the metadata fields:
