How to export a texture as jpeg or png? I downloaded my Blender model from the Internet, and it already had built-in textures for its materials and meshes.

How can I download the texture as a .png or .jpeg to edit it?
If I understand your question, you want to save on your hard drive a texture from a Blender project: open a window as UV image editor window, select the texture from the drop down menu (which contains all the images in the project) and choose "Image - Save as image".