If the person whose records you want are on the same plan as you, for example, a family plan, or added lines, all you need to do is to phone Verizon and ask for the records for the time period you want to look at. There may be a charge for this.
You can also set up an account to track these kinds of accounts. You do it online and fill in the details; make sure you have the phone of the person you want to track with you because it will receive a confirmation text with a password. You will then get all the information that you need about when the phone is used, who calls whom and where they are.
Another, equally unethical way, is to ring Verizon pretending to be the person whose records you want, obviously you need to be the same gender, otherwise it’s a bit of a giveaway, and you need to know their personal details including passwords.
If the reason you want someone else’s cell phone records is for far more serious reasons than trailing someone, for instance, they have gone missing, you can phone Verizon and explain the situation. Once you have emailed or faxed them the police report, you can ask for their records; they will probably also put a trace on the phone to find out when and where it was last used.
If you need someone else’s records for something like a litigation, you will need a subpoena.