Honestly, I'd say there are TONS of tutorials in which to start off with.
If I were you, I'd find one that you think has the most likely chance of piquing your interest, and working with it.
Be it how to make a cube in a 3D modeling system, or how to make a book; start somewhere you know may be basic, but something you know you can do.

I agree, youtube has plenty of tutorials and if you have a bit of spare change, you could always sign up with a subscription through lynda.com.
The site is filled with tutorials on all manner of computer programs and ranges from beginner to advanced tips and tricks.

I will say though, something like Dead Fantasy is not something that's going to happen overnight.. First Monty Oum is just crazy and really has an eye for choreography and I can't say for sure how long, but I'd be willing to bet that each of those videos represents weeks if not months of consecutive work.

One thing that might help is once you find yourself comfortable in a 3D software, like 3D Studio Max or Maya, or Blender if you want to go the free route, would be to see if you could find some pre-rigged models to practice with. Having a rigged model will make things way more easy to start animating with.

You mean ripping models? I've seen people say you can rip models from video games that your PC can handle, like the models from a PS2 game. Have you ever tried such a thing?

Well, yes. That is an option. I don't have any experience with ripping models other than with WoW Model Viewer personally.

But I was referring to finding models that people have built that have rigs inside them, ie; a skeletal structure that allows for easier animation. There are some you can find online for free that would serve to give practice in creating realistic movement in the program.