Download the latest APK from a trusted source like GitHub or the developer’s page (FBA4Droid is no longer on the Google Play Store due to policy changes, so you’ll need to sideload it. Enable "Install from unknown sources" in your Android settings).
Since arcade games are still commercial intellectual property, no "official" source distributes them for free. However, preservation communities maintain archives. When searching for "FBA4Droid ROMs", prioritize: fba4droid roms
A "ROM" is a digital dump of the read-only memory chip from an arcade board. But arcade ROMs are complex. A single game like The Simpsons Arcade might consist of 10+ files (program code, sound data, graphics tiles, sprite data). Download the latest APK from a trusted source