What software would I need to make stuff like this? (3D Animation and stuff)

You would need a great knowledge of Autodesk 3ds max, Maya, Zbrush and a few others but those are the most important tools that you need to know. 3Ds Max is known for having a very friendly UI and it's used in video gaming industry. Companies such as Epic Games and 2K Games use 3ds max for modeling/texturing/shaders. Maya's strengths are rigging and animation. Maya is used in CG movies such as in The Amazing Spiderman/Avatar etc. Maya is a very powerful software and if you know what you are doing, you can create some powerful CGs with it. Zbrush is used to create characters/animals. I've been using those 3D softwares for years and there are still a lot of things that I have never seen before. It takes time and dedication to learn these kind of softwares because they are very complex. I will edit this post later when I get home because I'm running late for a class.

The other person pretty much said the most popular apps, which are not the best, but you should start with them anyway because there is a lot of training/tutorials to do just about anything with them. Achieving anything remotely close to that will take you a lot of time. Do not even think that you will do something like that after starting up the software. You either need to enter a school of arts that there are professionals that will guide you, or learn it yourself(which will take even longer) from the internet. To do both these things you need to spend money to buy professional training + the software isn't free. It took me years to learn, but I was doing it as a hobby every once a while. It took me 6 years to be exact. Doing 3d is a lot of hard work and little reward. Rendering in 3d is computer intensive be prepared to leave your pc for days on at full force(hopefully you are doing this in the winter because you will be saving a little money on heating and such.)
Edited by windowszp - 10/23/12 at 4:13pm

Start with 3ds Max and if you are a student, you get it for free for 2 years I believe.

Since you are just getting started, then I guess it would be fine to use 3ds max on a laptop but when you start making complex models that are over a million polygons, I highly recommend to use a desktop for that because it will create a lot of heat. I would never do rendering or make complex models on a laptop because it heats up your laptop very quickly and that's never a good thing. Also, make sure you have a good graphics card on your laptop because the viewport in 3dsmax/Maya is hardware accelerated and it will use your gpu to render things in your viewport. If you have a slow graphics card, it will start lagging/freezing badly and it gets super annoying.
Edited by Capt - 10/24/12 at 9:56am

I'd start with 3ds max because it has a much easier user interface and it's a good program to learn the basics of 3d. Like I said in my first post, 3ds max is used in the video gaming industry because it's a lot easier to make 3d objects and then export them into map editors such as Hammer Editor (Valve's Source Engine) and Unreal Editor (Epic Game's Unreal Engine) . Maya is much more complicated because it is built with much more complicated things in mind such as rigging and animating. Maya has way more features than 3ds max because it can do so much more that the artists need to do their animations and rigging where in 3ds max those features are not there. You can start with Maya if you want but it will be more difficult to learn the basics and you will find yourself forgetting where most of the tools are the next day you open the program. The 3D field takes years to learn and like most people on the internet say, "one lifetime is not enough to learn it all". Even the highest paid 3d artists that work for Pixar/DreamWorks have never even see some of the tools in these programs because there is so much to learn.

3DS is a more powerful modelling tool.
Maya is a more powerful rigging (putting "smarts" in model, say physical properties, a skeleton through which the 3D mesh will deform around, which parts of a vehicle move and how/which direction-axis etc) + animation tool.
Both can do either, i.e. you can rig and animate models in 3DS, just like you can model complex geometries in Maya. 3D creation tools are not exclusive.

As well put by ppl with experience in this thread, getting the programs that were used to make such movies is step 1, if not .1 of many.

You need a lot of personal friction, experience and struggle with the thing just to grasp the basics. Without expert assistance, even if it is remote (aka forums, webinars etc) it will be hard to produce even single frames (stills/static images) of that complexity. People who do that, are called 3D artists for a reason, it is not a plug and play thing.

So going beyond the hardware and software limitations, you have to start organizing yourself, join specialized communities/forums with knowledgeable people that are willing to help you and perhaps start saving up for a school etc. If you would decide to stick with that field for a loooong time, at the end you will find out what most ppl in this industry find out the hard way: you cannot possibly do everything perfectly, so you will specialize in a field / part of the creative process: modelling, texturing, adding effects, rigging, animating, rendering, directing, editing. Just like full motion pictures, 3D movies (and stuff) usually have a team of people working hard behind them. Not that it is impossible for an individual to do it by himself, but because the sum of a team/system is greater than the sum of its parts.