If you're just recording audio, like narration or sound effects, we recommend using the free Rode Reporter app which is available on both Apple and Android. Change the settings to Standard Quality (48kHz 24-bit WAVE).
If you're recording video, MAVIS is a good app for iPhones that records at 1080p, 24fps. The free version of MAVIS allows you to control exposure and focus. You can buy additional features.
If you're recording video, Open Camera is a good free app for Android phones. Your first time opening the app, you'll have to follow the prompts to allow access to your phone's microphone, camera, and photos.
Another popularly recommend app for more advanced settings and recording quality is Filmic Pro. Filmic Pro is available on both Apple and Android devices. However, this is NOT a free application and therefore only recommended for those looking for an advanced production experience. You may achieve many of the same effects by editing your video in post-production. The guide for video editing and software applications is linked in the "Additional Resources" tab.