I'm trying to insert a photo into another photo and have it look like its on top of the other, but when I insert the second photo it inserts as a background with its own background. How do I get the second inserted photo to just sit over the other without its own background.
What you wrote does not make sense to me. There can be only one Background layer in a photoshop document. You insert images either using Place, Drag and Drop, or Paste. The inserted image will be a layer above the documents background layer. Photoshop's background is the a special bottom layer that does not support transparency it is always canvas size. An Inserted images will be a Normal layer or Smart Object layer above Photoshop Background layer if the document has a Background layer. A document is not required to have a background layer.
If you insert a Image the has a transparent background ie a PNG, a PSD, a Gif etc. They are file type that supports transparency a Transparent background is possible, If an image has a transparent background, when you insert the image into an others image it will have a transparent background. A raster Imags layer may not have any transparency.
Jpeg file format does not support transparency. Jpeg image do not have any transparency. Subject matter always have a background color.