There are a few ways to get an image into InDesign with a transparent background.
The First Way
1. You will have to make sure there is no "background" layer. Do this by double clicking the background layer, when the dialog box comes up, rename the layer. from this point you can delete that layer. Erase the areas on your existing layers that you would like to be transparent. As long as your other layers do not cover the entire canvas, you will see the checkerboard background. This notes transparency.
2. Save as a .PSD.
3. Drag or place the saved file into InDesgin.
The Second Way - Clipping Paths (used on photos and compositions by pros in the print world)
1. From the path menu/tab create a New Path, either with the drop-down menu in the top right corner or the New Path icon at the bottom of the menu which looks like a folded page.
2. Name your path, something like Clipping Path.
3. Draw a path around your object, with the Pen Tool.
4.Draw the knock-outs/holes.
5.From the drop-down menu in the top right corner, select Clipping Path...
6. Click OK.
7. Save your document as a TIF
8. Drag or place the saved file into InDesgin.