Blender 3D is a fantastic (free! open source!) tool that can model 3D computer-generated scenes and characters, render high-quality videos, as well as games.
The interface is not easy to learn. The first time I opened up Blender, I played with it, got frustrated with the interface, and quit. I found much better tutorials and examples in the Half-Life 2 modding community, so I made my first serious 3D efforts as Half LIfe 2 mods. The difficulty of sharing those creations, and the fact that my students would have to purchase copies of the game to create levels, made me switch back to (open source, flexible, powerful) Blender 3D.
If what you want to do is make complex 3D environments quickly, I’d recommend Google’s Sketchup. It does not let you create a game, and the output is cartoonish rather than realistic, but if you just want to build things in 3D space, the interface is much simpler.
CG Cookie offers a very careful introduction to all parts of Blender 3D, starting with installing the software, and continuing through the interface, modeling, materials, animation, rendering, and lighting.
Video #2, “Interface and Navigation” is absolutely vital if you hope to do anything at all in Blender 3D — it’s very thorough, and very efficient, but to get the full lesson, you have to be particularly motivated, or unusually interested in things like interfaces and controls.
Video #3, “Intro to Modeling” continues to introduce more of the interface, with the specific focus of creating different kinds of shapes.
I recommend that beginners watch all 7 videos, but if you’re itching to start a game, after watching video 3 you are probably ready to watch
Johnathan Williamson’s Create a Basic Game video.
(His video carefully documents every mouse click and keypress, so even though he’s talking to Blender users with some experience, his videos are also useful to beginners.)
I found David Ward’s game engine tutorial very useful; the only problem is that he doesn’t walk through how to model his character. (For a more detailed introduction to character-modleing skills, watch Ward’s how to model an alien.)
Another good tutorials, but not necessarily the best place for beginners: a tutorial for a plank-based demolition game, Planks Physics Games