If it is within the 14 day return windows, you are entitled to exchange your device for a brand new device. If you pick the same model, you should be able to just swap it in a store. If you want another device, be advised the $35 restocking fee will apply.
After the 14 days, you are then within the 1 year manufacturer's warranty, which covers any defects an outside influence did not cause (damage you did not do yourself). You must call VZW Tech Support at 1-800-922-0204 and select option 3. Replacements are the same device, as the warranty is not offered by VZW, but by the phone manufacturer. VZW no longer has the "Three Strike Rule" where they will give you a different phone if you have had 3 or more replacements of your current phone. When you send back your defective phone, then will charge you $99-$299 if your phone has major damage (minor wear and tear does not count). ***FOR 99% OF ISSUES YOU ARE REQUIRED TO TROUBLESHOOT THE ISSUE WITH TECH SUPPORT BEFORE A REPLACEMENT CAN BE SENT. YOU HAVE BEEN WARNED.***
The insurance comes into play in two ways: 1. You drop your phone and it breaks. This is not covered by warranty. You must contact Asurion (who provides cell phone insurance) about making a claim, provided you already have insurance. 2. You are outside of the 1 year manufacturer's warranty/do not have any extended warranty, and your device malfunctions not due to outside influence. All claims to Asurion to have a deductible, like any other type of insurance.
I always recommend everyone get the Total Equipment Coverage (TEC) that Verizon offers, as it gives both insurance coverage if you damage your phone, but it also adds an extended warranty THAT NEVER ENDS until you remove the TEC feature. It also comes with perks: Asurion provides a free application for smartphones called My Mobile Recovery that allows for remote locking/wiping/locating to a device. Not only that, but it also means that if your phone ever malfunctions (not due to outside influence) and you have to call VZW to get a replacement, you get free overnight shipping on the replacement (as opposed to 5 day economy shipping).