Despite the progress in 3D and hyper-realistic animation, 2D is still used in major cinema and cartoon productions, both for entertainment and educational purposes.
OpenToonz is a free, open-source program that allows you to create your own 2D animations. It has basic drawing tools for you to create your sequences frame by frame. These tools are very akin to the ones you can find in other drawing software, from MS Paint to Photoshop, so if you are familiar with these programs, then you won't have any problem in using this one.
At startup, the program asks you if you want to create a new project or if you want to open an existing one. Once you have chosen the corresponding option, the main interface will appear, showing the canvas and the drawing tools.
Please don't get fooled by its apparent simplicity; the program has been used to produce major cinema productions, so it has many advanced tools. To take advantage of all of them, you need at least a basic knowledge of the animation process, since these tools aren't very intuitive.
Once you have created your animation, you can play it to see if it needs any correction. If so, you can choose the corresponding frame(s) and make all the corresponding modifications.
In sum, this is a free tool for advanced users. A great advantage is that, since it is open source, you can take the code and customize it to better suit your needs. Of course, to do so, you will need a good programming knowledge.
If you are looking for an effective and affordable animation tool, you will love this one.