Introduction

This article aims to teach you the basics about how games are made, and what they're made of.  The individual fields of game development will be introduced and explained briefly in a simple way, without getting too technical or confusing.  For those who want to jump in and start learning, resources (tutorials, software, stuff like that) will be linked as well.

Note:  Please keep this article "Under Review" while it is being completed with help from the community!  This article still needs a lot of work and is meant to serve as a starting point for beginners. Specifically, the Music and Sound section and the Resources section are in need of some love.  Expect to see many changes in the coming days. If you're not part of the GameDev 'Crossbones+' group, but can offer materials you'd like to see added to the Resources section, please PM me about it.

The Fields of Game Development

It takes a set of rather unique skills to create a full game; they're made of a lot of parts.  This is why game studios often have teams dedicated to making games, with employees from all the necessary fields.  It's hard to make even a simple game all by yourself, though it's getting easier with the advance of technology.

Let me introduce you to these fields individually.  Once you're introduced, there will be resources to see you on your way to learning whichever field you choose.

Programming

Programming makes the gameplay itself, and all of the 'gameplay logic'. Jumping, moving, picking up new weapons, and saving/loading your game wouldn't be possible without a programmer.
Essentially, programmers tell the computer what they want it to do. Computers don't speak regular, human languages, though. They aren't that smart. You have to use a programming language to communicate with them, and instead of just using sentences, you use code.

This is essentially what programming is, but in order to really decide if you like it or not, you should just look at some beginner tutorials and get the basic hang of actually writing code and how the code works, because that kind of stuff is hard to explain in a few sentences.

Art

Games must have some form of art (conventionally). The kind of art you need depends on whether you're making a 2D game or a 3D game.

2D games use 2D images, made in Photoshop, Microsoft Paint, GraphicsGale, GIMP, and other such programs. The programmer deals with drawing the images to the screen and moving them based on the game mechanics. These images are usually animated, such as to make a character jump, or swing a weapon.  This is done by drawing multiple instances of the image, all in different poses as the image does whatever you're animating it to do.

3D games use a mixture of 2D images and 3D 'models'. Models are made of vertices, which are just "places" or "points". Those vertices (also knows as vertexes, or verts) are connected to each other to form triangles (tris), made of 3 vertices, and/or polygons (polys), made of 4 vertices. Some programs allow you to make polygons out of more than 4 vertices. Models are made with programs like Blender, 3DS Max, and Maya.

3D games also have to animate some of their models, like the player and the enemies, otherwise your game would be made of a bunch of still objects sliding around on the floor instead of walking or running (and that would probably be lame).  Animations are commonly done by binding a set of vertices to a "bone", and moving all of those vertices at the same time just by moving that bone.
So you'd have a bone for the upper left arm, a bone for the lower left arm, a bone for the upper body, a few bones for each leg, and so on.  You can move those bones into 'poses', like placing a foot forward.  You make a lot of these poses and the software you're using to model and animate will move from one pose to the next when you play the animation.  So you could have one pose with the character standing, the next with the right leg lifted, then the right leg set down, then the left leg lifted, set down, and so on.

3D games also have to put textures on their models. Textures are made like 2D images, and then they're "put on" the model. Modeling programs often provide you with the ability to "UV map" your model. This is how you decide where your textures are placed. It's hard to explain in text, but essentially, you tell your program how the texture should be laid out across all of the tris and/or polys that make up your model.
Textures can be the actual colors that draw the character, like their black-and-white suit and tie, their actual face, like their eyes and eyeballs and their lips, and so on.  Those kinds of textures are sometimes called 'skins'.
Other times, your textures are like tree bark that you wrap around your tree models, or rocky textures that you put on all your stones and mountains.

Music and Sound

Note:  Unfinished.  I don't know enough about music and sound to make this section!  Other members will have to fill in for me.

Writing

Game writers deal with the characters, dialog, the lore of the world, and so on.
But you can't just drag a novel writer in and tell them to write up your game.  Games are much different than novels or movies.  You have a lot of other means of communicating your narrative to players.  The art style, the mechanics themselves, the music and sound, they all have an effect on the mood and environment of the story.  Game writers, or "game narrative designers" as some people call them (I think it's more fitting, too), aren't just going to be writing text.  There's a lot more to game narrative than text!

Note:  Unfinished.  I've heard that game companies often don't actually seek out writers, and you kind of have to work your way up if you ever want to be a game writer (like it is with game designers).  However, I'm not in the industry, so I need someone to clarify here.

Resources

Programming

The most important thing is to pick something and stick to it until you're good enough to comfortably switch to other things that expand your abilities.  It's more important that you know general programming fundamentals rather than lots of languages.  Get really good at one language, not mediocre at three different ones!

If you're going to write your code, you'll want a program dedicated to writing code, preferably one that supports debugging (telling you where you've made errors to help you fix them) in the language you're using.  A program like this is usually called an 'IDE', which stands for Integrated Development Environment.

It's suggested that, before you go and get into developing games, you learn the fundamentals of programming.  This will help to establish a firm ground for the rest of your learning because it will be the kind of stuff that applies to programming in general, not a specific language.

Once you're ready, a lot of people will suggest you start with 2D games, because they're often much simpler than 3D games.  They cut out some of the things you'd have to worry about that may overwhelm you.  3D games also involve more math than 2D games.
It's suggested that you start by programming small games, like clones of Tetris, Pac-Man, Pong, Breakout, etc.
This will make sure you aren't delving too deep before you're ready, and will help to keep you motivated with quick results.

Generic Programming and Fundamentals:
Before trying

Note:  Unfinished.  My original route to learning how to program was hackneyed and disorganized, so unfortunately, I'm not the one who would have any resources like this lying around.

C# as a language, XNA as an 'engine':
You can hop into making 2D games with C# as your programming language, using Microsoft Visual Studio C# Express, a free IDE for writing C# code.
Here is the Microsoft official tutorial on making a simple game with C# and XNA.
The tutorial tells you to get Visual Studio to write your code and to make sure you have XNA installed.
Get Visual Studio C# 2010 Express (click on "Visual C# 2010 Express")
Get Microsoft XNA 4.0: specifically here, though you might want to poke around here as well.

Art

(3D) Blender
Blender is a great, totally free and open-source program that can be used to model, animate, rig, and UV map (among other things).

Here is the official website, where you can find a link to download Blender.

The user 'cgboorman' on YouTube has a very helpful beginner's tutorial series for Blender.  If you're just getting started with Blender and/or 3D modeling, I highly recommend his videos.  Here is a link to the entire playlist on YouTube, with all the tutorial videos in it.

Blender Cookie is a website with lots of tutorials for using Blender.

The official Blender website tutorial page has a large collection of tutorials in various categories, from modeling to animation to lighting.  It also has beginner tutorials to teach you the interface, if you don't want to use the videos I linked above.

Music and Sound

Note:  Unfinished.

Writing

Note:  Unfinished.

Article Update Log

27 March 2013: Cleaned up the Resources/Programming introduction
26 March 2013: Added a link to Resources/Art/Blender
22 March 2013: Initial release