Choosing a Look and Feel
First, you'll want to decide on an overall look and feel for your game. For example, do you want a dark, gritty look, or a smooth, flat-shaded look? Realistic or surreal? Or, you could get more creative and do a sketchy look or something that looks like a 1950s black-and-white detective film. A lot of this depends on the target audience. An adult might enjoy a darker game with dramatic lighting and shadows, but a younger kid might prefer a bright, colorful game.
Looking for Inspiration
Sometimes inspiration for your game's look and feel can be the hardest. Think about what games you like to play and also movies and TV shows you like to watch. Sci-fi films generally pull off some great stunts and effects that are inspiring, but also think about other genres, such as westerns, mysteries, or even sports. Take a look at the world around you for inspiration. Would it be fun to create a tag game in an environment based off your apartment building? Or an adventure game in a setting like the woods and creek near your house? Finally, don't forget about the more classical forms of inspiration you'll find at an art museum. Imagine playing a game that looks like Van Gogh's Starry Night or one of Magritte's strange worlds. And Salvador Dali's melting clocks are always a popular surreal favorite. While you're busy being inspired by the world around you, keep in mind that there's a fine line between finding inspiration and ripping off something. It's okay to be inspired by the latest blockbuster game or movie, as long as you're not creating a game that looks a little bit too much like it.
Do you want some textures in your game to look like a cartoon while others look dark and realistic? Probably not. Likewise, you wouldn't want a weapon-toting demon fighter to make cheesy "boing" sounds when jumping. It's generally a good idea to make sure your game art, interface art, and sounds mesh together well. For example, try to keep textures for a 3D game at similar brightness levels (because lighting is done in-game). Also, the user interface should have some sort of consistency with the overall look of the game. For example, a cartoon-like game might have colorful buttons that are big and shiny, while a first-person shooter might have dark buttons with eerie shadows.