To play a song that is not in your iTunes/Music app library, simply drag & drop a file from the Finder window onto one of the turntables in djay. You can add a whole folder to the left panel of the Finder library by drag & dropping. You can also drag one or more songs from the Finder into the Automix Queue in djay.
You can search for songs through the search bar in the Finder section. For advanced search options click on the down-arrow near the 🔍. You can search from all files added to djay's Finder Library or you can search within a specific folder.