I have tiff. files that are 72dpi. In order to put them into my book for publication they have to be 300dpi. How do I increase the dpi without changing the size of the image. When I go to PhotoShop and change the dpi the picture of course shrinks. Then when I put it into my document and enlarge it to the appropriate size the dpi goes back down.Is there a way to keep the size but put the dpi at a level the printer wants.
To put it plainly, you can't.
Or rather it doesn't work that way. An image has an existing number of pixels.
When you increase the PPI without resampling, you tell that image to condense the same number of pixels into a "tighter" field. Thus reducing the image size.
If you alter the PPI and use resample the application throws in all the extra pixels needed to maintain the dimensions as well as the new PPI you want. The application decides what pixels it should create. This most often results in an image of less quality.
The best option for you is to use higher PPI images from the start. I do realize this is not the answer you want. Your printer is telling you the images will look horrible unless you use better quality images from the beginning. You can't "repair" or "adjust" low resolution images to magically be high resolution and look the same.
It's true you can't upscale the resolution of an image in terms of clarity because the information just isn't there (aside from Photoshop's clever upscaling extrapolation, which can smooth things over a bit).
However, if you just want to change the dpi settings without changing the size of the image (disregarding the resolution of the existing content), it's very easy to do (in Photoshop CC 2015, anyway):
Just click the little gear-looking settings icon in the upper right of the 'image size' dialogue box and you'll get an option to scale styles, which will allow you to change the resolution without changing the size of the image. Check the resample box. Cheers!