How do you approach designing a user interface that is both functional and visually appealing for a mobile app?

Instead of writing something really big,

Research some creative designs in your niche.
try to be creative and come up with your design based on your research.
3rd point, work on usability, actually trying to use, it, are colors having issues, are buttons visible?
are the items easily in reach etc.

Overview
The first step while creating an App is obtain the vision for the project, to understand and define the goals aimed be reached with the application. Most common questions are:

- What is about?
- What the users will do inside the app?
- What are the functions of the app?

Projects Goals
Based on these questions the designer will be able to analyse the project, make annotations about the functionalities and what options will be available inside the app. This is the most important step aimed to colect all requirements of the app.

Ui/Ux
After collect the requirements, all ideas will be added in a low fidelity wireframe. The wireframe is a first look of the project that contains all functionalities and the user flow, the user flow contains all things related to the user experience: positions of elements, journey between the pages and also display well planned icons that will represents the idea of that respective function.

Brand Guidelines
After define the wireframe, make tests in navigability and define the best flow to make the things quickly and easy to be understand, is time to work in the design of the project. At this final step, to make sure the app represents the identity of the company, the designer will apply the logo and brand guides. The market trends, competitors and target audience is also taken in consideration in terms of design to make sure the project is appealing to that audience.