Tyluna runs right in your browser — on your phone, tablet, or computer, with nothing to install. No native iOS or Android app exists yet.
If you want it to feel more like an app, add it to your home screen:
Open Tyluna in Safari (iPhone) or Chrome (Android)
Tap the Share (iOS) or Menu (Android) button
Choose "Add to Home Screen"
It'll open full-screen from your home screen from then on, just like an app.