You can create your own 3D video game without spending any money! Let me tell you just how.

First, every game is powered by an engine, so you'll need to pick an engine. There are quite a few good ones on the market. I highly recommend you use one called Unity 3D. You may have heard of it already. It's a very professional game engine, and it's free. It is very popular among both pros and beginners. It also has an Asset Store with lots of free and paid assets available. However, if you like open source, then I suggest you check out the Godot engine. One of the nice things about Godot is it works on Linux, as well as Mac and Windows.

The next thing you will need is some kind of content creation software, to make the things that will go in your game. Most professional game developers use expensive software such as Autodesk Maya, but there is an excellent free alternative: Blender. It's fast, it's free, and there are a vast amount of tutorials to help get you started. By the way, if you are thinking of using Google Sketchup, I would highly advise against it. Sketchup is not a game content creation tool, and although it is free and easy to use, it lacks most features needed for making game models.

The last essential tool is Gimp, which is a free tool that allows you to create textures and manipulate images. Without textures, your 3D models will be bland and colorless. 

Now you have a set of tools which you can use to create your game, but you still have to learn how to use these tools. Let's start with Unity 3D. Where can we find free tutorials on Unity? Well, they have lots of free training on their website where you can learn all about Unity. You want to learn Blender? I recommend Blender Cookie and BlenderGuru. How about Gimp? There are some tutorials on the Gimp website, and you can also find lots at Gimpology.

One piece of advice before you start creating your awesome game: keep it small. That doesn't mean it has to be lame, it can be really great. But it still needs to be small. I know a lot of beginners hear this advice, but they ignore it. They try to make their own MMOFPS. When I was starting out, I wanted to make big games. Later I learned that there is a reason these "big" games are created by teams of sometimes hundreds of people. They are hard to make. Do not attempt to create an MMO. Do not try to make something huge and spectacular. Your goal should be to make something that is fun, that people will play. After all, if a game isn't fun, what good is it?