To become more technical what we are referring to is 2D or 3D animation. 3D being 3 dimensional by way of the order of the images be presented. Each movement is known as a frame. One frame very gradually moves onto the next and give us the illusion that the object is moving. The frames are then presented moving from one to the next very quickly.
To create this effect by hand or as we refer to the 2D was painstakingly consuming. The artist would have to draw a new picture each time the object moved in any way. Then all of these photos would be put together consecutively. These were called cell animation and hand drawn animation. Although it was detailed and a great deal of work, it was well respected by the true animator and received with pleasure by the viewer.
Cartoons have been based on 2Dimensional art for years. With the inception of the computer not long after came the capabilities for 3D. This does not mean that 2D still does not have its place of importance. Nor does it mean there is no skill involved. If one thinks that, an individual that who has no artistic basis can sit down and do 3D animation just by learning the software this is simply not the case.
To create 3D animation it requires the use of complex software. All of the characters are designed by way of the computer and hand drawing is not a consideration. It will progress through a series of steps before the project will be completed. The individual who is responsible for this project must have a thorough understanding of each and every step in order to reach the desired results.
There are many standard software programs that are used for 3D animation. There are several on the market. They all vary as to capabilities and complexity. If you have a real interest in this type of art, then you could start with a very basic program. As you, master the one move on up to the level. Remember though this does not replace the artistic eye. You need to be able to discern that the character looks perfect during every step of the way to becoming completed. If you are not able to critique your own work then you are not going to get good results. If you seem to have a knack for drawing but have had no training you may want to consider taking some art courses and at least learning the basics before you attempt 3D animation.
Finally, you should be aware that it is not just a matter of mastering the software. Large production companies have had their own software designed specifically for them. If you to approach these companies for a job then you would most certainly needs the basics as we have just outlined.