You may want to do some research on the differences between RGB and CMYK colors. Your screen is in RGB and your printed design is (usually) CMYK. I say "usually" because some printers use PMS, which allows for more vivid colors than CMYK, but neither will look as vivid as your RGB design does on-screen.
If you know that you are designing for print, configure Photoshop accordingly, when creating a new document:
To convert an existing document's color mode, use the option pictured below.
Also, if it's not already at 300 dpi, set it to that as well, via the Image Size window (IMAGE > IMAGE SIZE).