I recieved a warranty iphone 5 from verizion because my last one died. I'm trying to set up the new phone, and after setting language and country it tells me to plug in to a computer with itunes. I have never plugged in before, and I can't get any farther

Start over by doing a reset.

Reset: Hold the Sleep/Wake and Home buttons and don’t let go until the screen goes dark and the Apple logo appears (no data will be lost)

Do you have a backup of the phone this is replacing?

If you have never connected to a computer then I assume you either have an iCloud backup or none at all.

When you get to the setup screen choose Restore from iCloud Backup if you have one, if not, Set Up as New Phone. If you choose Restore from iTunes Backup you will get the connect to iTunes screen.

Does it look like this?

If so, it is in Recovery Mode and there is no other choice but to connect to iTunes to be restored.

It sounds like your phone has not been activated with Verizon.

Do you still have access to the SIM card from your old phone?

If you do, turn off the phone, insert your SIM card then power it back on.

If not, connect it to iTunes on a computer and activate it.