My goal is to make characters for games, and I have been watching this video series https://www.youtube.com/playlist?list=PLFt_AvWsXl0eTHFZ2XPkM... - I recommend the 5 Blender Character Animation videos. Tremendously helpful.
In my opinion the key is, like learning most things, a little bit every day.
My starting point was http://www.blenderguru.com/ (for general tips and tricks), reading about ray tracing(for understanding why my renders were not up to the mark), anatomy of physical shapes(for sculpting) and watching a lot of behind the scene VFX breakdown videos(to understand their construction). Frankly, my humble computer back then was not capable of running 3DS Max or Maya.
Apart from this, a lot of articles regarding photography helped. A keen attention to detail and huge amounts of patience is required(while watching your renders take hours if you have the wrong graphics card).
It also has a fairly high learning curve at first, but there's a huge community built around it[2]. Andrew price has some very high quality tutorials[3]
1. https://www.blender.org 2. http://blenderartists.org 3. https://blenderguru.com
What sucks is they got rid of the Personal Learning Edition of Maya, so getting a legit copy just to learn isn't as simple. They do have a 30 day trial. Maya's documentation is still pretty solid for reference, just not for learning, so if you're curious what a menu or button does you can find out easily.
I think for learning anything new it's best to have a project like that "web-dev to 3d post" mentioned in another comment and focus on what you need to accomplish. I've also heard Cinema4d is a lot less intimidating to learn and has most of the basic things you'd want.
The blender communities my sibling mentioned are a great kicking off point with some high quality tutorials and resources. The blender wiki is also decent, but unless it has been updated recently, I tend to find it out if date. There are also tons of tutorials for learning the basics on YouTube.
Without having taken a 3D modeling course, I would say that following tutorials that teach both using the tool (blender, 3DS, Maya) and making basic models is a good place to start. From there, find tutorials to accomplish tasks that interest you: animation, texturing, organic modeling, rendering, etc.
I used AutoCAD in university and that is the extent of my knowledge on these matters.
I've since switched to Modo (affordable indie licenses via Steam) but find both programs to be more modern and adaptive to my workflow than Maya and Max -- however, if industry standards are important to you, there is no avoiding the Autodesk Twins...
Not sure I feel great about that but I treated it the way I treated Photoshop and friends for years: cracked copies while learning and then at some point I was using it enough that I bought a legit copy of CS6 through work at a discount.
If I ever do more than fiddle around with C4D I'll look into buying a copy. It's just hard to come up with $1000 for the minimum version that supports global illumination (which I was trying to learn about).
Moral and legal issues aside, though, I found it a lot easier to learn than others I'd tried and it even made some other programs like Unreal Engine easier to learn.
It has a reputation of being difficult or long to learn, but I disagree. I find it way more intuitive, as you can see step by step what is happening. Their doc also has loads of examples and there are nice forums to ask for help (http://odforce.net and http://www.sidefx.com/forum).
If you have a logical mind, it should appear straightforward.
From my little window in the industry it's indispensable for FX and simulation (water, fire, destruction), but the tools for modelling, texturing, and animation just aren't worth the time. I don't know anyone who uses it for that or would reccomend it for those things.
I've gone through their basic tutorials. It's really nice to make procedural reusable things (a ladder that will create rungs based on the height), but I can't even imagine trying to model something organic.
I did commercials where animators where taught to use it, and that was a success in my opinion. They were happy because the animation tools are basically the same and the rigs were updated faster than they would be on other packages.
And it is true I've rarely seen models being done in Houdini. The only time I did one was for this commercial (https://vimeo.com/17808406), where the character is quite procedural. Had it been a more classical character, a Maya modeller would have done it.