Step 1: Download Kodi 16.0 from (
https://kodi.tv/download/), be sure to pick the right version for the equipment you are installing it on (Windows, Mac, Etc.)
Step 2: Verify the Skin you are using is compatible with Kodi 16. If not, or you are unsure, change your Skin to the default (Confluence).
Step 3: Beside your Skin, you might also look at all your Add-On's and verify they work with Kodi 16 as well.
Step 4: Exit out of Kodi 15.2, then run the installation for Kodi 16, it should install over your existing version without any issues.
Step 5: Launch Kodi (it should now be version 16 'Jarvis'). Check your addon's to verify they are working correctly. If not, see the appropriate sub-forum here. Same goes for your desired Skin, check to see if it has a 'Jarvis' version.
Enjoy your new Kodi build.
Can there be problems or issues, sure, but if you follow the above, you should be ahead of the game. And since you didn't say if you installed your Kodi 15.2 yourself, or bought a system that was loaded with it already, that might also make a difference on how smoothly your upgrade will go.