How to use a Photoshop file in InDesign for Printing?

If your PSD contains any vector information, don't place it in the InDesign layout. Save as a PDF instead, and place the PDF. The reason for this is that a placed PSD is always a raster image in InDesign, because Id uses the raster layer that Photoshop saves within the PSD. A PDF retains all the vector information and makes it available to InDesign. A quick test will demonstrate the difference. I discussed this point here

Note that a Smart Object, even if the image it contains is a vector, always exports as a raster image, even to PDF, so create text and vectors as actual text or shape layers.

There are some peculiarities that you must be aware of:

• Spot colors must be Spot Channels (New Spot Channel from the Channels Panel flyout menu). Simply assigning a PMS color to an object in a regular Photoshop layer results in an RGB representation of the color; it won't show up as a spot color in any other application.
• Spot color channel data in a Photoshop PDF will not show up in InDesign unless you turn on 'Overprint Preview` from the View menu. The PMS swatches will appear in the Swatches Panel, though.
• Because spot colors can only be transferred from Photoshop [to the PDF] to InDesign as spot channels, which are always raster, the PDF technique won't help with PMS text or vectors. Create spot color text or vector graphics in InDesign

save the artwork as filename.psd from photoshop and open indesign clicl on < File > than click on < Place> or CMD D to place the artwork in INdesign and you can export the file as PDF (print qaility) for production.