If the information you need is not still on your phone (saved text messages, or call history), and you are the account owner, you can log in to your account and view the history there. Go to View Bill, and then Voice, or Messaging details. If you are not the account owner, then you will need to get the log in information from the owner or they can assign you as an account manager to give you access.
I'm not sure if this is available if you have a pre-paid account.
Online in your Myverizon account you can see who, when and where you made calls. You can see who you texted and when and who you got text from. You cant read the text on Myverizon site.
There are apps that will back up all your text to your email. Search in Google play store for a text backup app, there are many.