When one begins the character design process, what are good starting points? Are there well known methodologies or systems to help in this process? How does the design process work in game industry, and are there big differences between the approaches different game producers use?
Imagine writing a book. If you can put together a very short story about your character (1-2 pages), hand it off to somebody and they start to feel for this character, you win...
Your goal is developing a full-blown character that you could see in the real world. That means you are going to want to break down every component of a real world person into bits and pieces and use that model to mold look and behavior of your own character for a game.
When you think about describing yourself, or somebody you see, what do you think about? Well, immediately our attention is drawn to what we can see. This is a good place to start.
Don't ignore details... Short fingers? Scars? Tattoos? Missing eyeball? One leg? Tearful body odor?
You can now use those descriptors to assist in bringing your character a personality.
If you're designing a combat game, you can take the fact that you know your character has scars to describe a hard-fought battle the character was in back during Vietnam. Now that we know that, maybe your character has PTSD which will influence certain game mechanics.
If you're developing a puzzle game, maybe your character got those scars from a science experiment gone wrong.
The goal is getting all of the possible creative juice out of you that describes every single detail that you possible can about this character. Give your other designers all of the information that they could possibly need to fit your character into the game world.
If an Artist is modeling your character they can simply look at your descriptors and recognize the look. They can read a short bio and realize that this guy is a thug or an innocent/clumsy scientist.
If a musician needs to compose a piece that focuses on your character, they can discern the mood they need from reading a short bio.
I wholeheartedly recommend Better game characters by design: a psychological approach by Katherine Isbister
It covers the whole design process, from cultural preferences to physical features, in exhaustive details. It also differentiates PC design from NPC design, details the psycho-sociological aspects of each of the design choices, and explains how to evaluate your character design.
An essential read.