Could anyone please tell me how to make static backgrounds for 3D character skins or shirts like this in Chowder from Cartoon Network? To understand clearly, please, show me your explanation in a picture or a gif.
Here is a commonly used technique shown in a very simple material:
The technique involves using a separate object, in this case an empty to provide the coordinates of the texture. If you don't move the empty, then the texture stays in place as you move the object:
Here I have used a Voronoi texture node, but you can replace this with any texture node, including an image texture. To prepare, place an empty at the origin, and set the Object field of the Texture Coordinates node to that empty. Use the Object output of the Texture Coordinates node as the vector of your texture.