Determine what kind of game it is you're scoring. If possible, watch clips of the gameplay, look at concept art and listen to its sound effects. This will affect every single aspect of the music you write for it.
Flesh out a basic recurring melody for the game, often called the "theme song." It doesn't have to be a fully orchestrated track, but getting the game developer's approval on the main melody will make your job much easier later on.
Split the parts of the game that require scoring (generally a good chunk of any game) into manageable and noticeably differentiated chunks. For example, all the parts of the game requiring thoughtful, moody background music can be separated from the parts requiring frenetic action songs. This, too, will make your job easier during the actual songwriting part.
Write the music for each section of the game according to the required artistic concept for that section, and keep meticulous notes on which song is for which part of the game. The most common way to do this is by naming the songs according to where in the game they occur.
Give voice to your score using either a music-creation software capable of producing all the instruments you've written into the music or an actual orchestra of paid musicians. Record the music into adaptable, high-quality format like Ogg Vorbis or WAV, and package them together for the game developer.