In Adobe Illustrator, you use a "Clipping Mask". To do this, place the photo in your layout and then draw an ordinary box on top of it. Any box will do, but it must be on top of the photo. Select both objects and go to Object - Clipping Mask - Make
You can adjust the size of the image (or the frame if you prefer) by using the selection tool. Just grab a corner and drag. If you want to change the shape of the box, use the direct select tool. If you want to move the picture around in the box, use the direct select too, also.
This is an advanced technique in Adobe Illustrator, but one well worth learning, as it makes placing, sizing, and cropping photos very easy. And you don't need InDesign to do it!