We all need sleep and although it's difficult with a new baby, you can work together to ensure you both get some rest at least.
Share the feeding
Even with breastfeeding, you can express milk and store it in the fridge so you can both share the night feeds. If one does the 4am feed the other can do the midnight feed to allow you both to get some rest.
Go to bed early
You probably find yourself dozing off around 8pm, so take yourself off to bed and get some sleep while you can.
Get a routine
Try to get into a routine as quickly as possible. Humans are creatures of habit and if we do something regularly our bodies soon get used to it and the lack of sleep will become more bearable.
Try to relax before bedtime. You'll never get to sleep if you're stressed, lying waiting for the baby to wake up. Don't worry, if they wake, you'll hear them. Have a warm bath and a warm drink to help you relax.
Lay off the booze
Speaking of which, lay off the booze for a while. You might think that third glass of wine will help you sleep, but you'll think differently when you get woken up at 2am. Newborns and hangovers are not friends.
Eat as healthily as you can every day. Try and avoid heavy meals that make you feel sluggish in the day.
Get it where you can
Grab rest and sleep when it's available. If the baby is asleep, the two of you can have a lie down too. As much as there may be things you want to get done while baby sleeps, if you're exhausted the best thing you can do is get some rest too.
Have the night off
Give each other the occasional complete night off from feeding, so you get turns at going to bed early and sleeping through all night, it will help to refresh you both.
Take baby out
Even if it's just for an hour, take baby for a walk or to do the shopping and leave your partner to have a lie down in the afternoon it works both ways and you can both give each other the odd hour or two to yourselves.
Get some help with baby and other stuff that needs doing, whether its grandparents or friends, those closest to you are often happy to help out, so let them.