how can I retrieve contacts I accidently deleted from my phone

If those contacts were part of your last iCloud backup, then you can restore your phone using that backup. Otherwise, they're gone.

How do you retrieve them with a backup? Just plug it in?

contacts are not stored in a backup, they are synced with iCloud. toggle contacts in the settings for iCloud and choose merge when it asks. if they are in iCloud, they will come back.

inked mommy is 100% correct