In Photoshop using a Clipping path or Alpha Channel. After that, place it in InDesign. InDesign is a Page Layout program, not an image editor.
With Photoshop if your image is a bitmap; with Illustrator if your image is an Illustrator vector image. For other types, use the software that created it in the first place. "Image" is kind of a broad term, and the exact procedure depends on what type of image it is.
InDesign is page layout software, and you cannot edit images with it, generally speaking.