Samsung.com provides the official manuals for the Galaxy S4, as of 2015. The website provides multiple versions of manuals for variations of the phone model.
From the Samsung.com home page, click on Owners & Support, then click on Manuals & Downloads. Enter your product's model number or "Galaxy S4" in the search bar, then select the link for your phone model. Alternatively, click on Cell Phones under Mobile, select your phone carrier and phone model, then click on the Get Downloads button. Click on the Download (PDF) button corresponding to the version of the manual that fits your needs. If prompted to do so, click on the Continue button.