Life with a new baby is a 24 hour a day undertaking, but there is light at the end of the tunnel. Usually by the time the baby reaches the age of 3 months, they are sleeping for longer stretches, sometimes as long as five hours at a time. And by age 6 months, that could possibly stretch into nine or 12 hours.
Work out a schedule for baby duty that is fair and equitable to both partners: Perhaps a nightly schedule where each partner is on duty for three hours at a time. If the baby is breast fed, your partner might handle the night time nappy changes. If the baby is bottle fed, you could take turns feeding the baby.
In the meantime, while you're waiting for the time when baby will sleep through the night, be creative and sneak in as much sleep as you can. Try to sleep when the baby does. If friends or family come to visit, don't offer to be that gracious host. Let them care for the baby while you take that much need nap.
Don't share your bed with the baby other than for feeding or comforting. And sometimes it is okay to delay going to get the baby. They may be just fussing or settling down for the night.