How you calm down a fussy baby at night depends on what is making the baby fussy at night.
Sometimes a baby may need a diaper change, need a feeding, or just wants comfort or could be suffering from colic.
Babies will normally cry a lot at night for the first 6 months of their lives which is normal and will stop as the baby gets older.
If your baby is fussy at night you should check their diaper and see if they need changed or see if they're hungry by offering them a bottle and if that is not it then you can try picking the baby up and rocking them in a rocking chair in your lap which can sometimes help the baby calm down and go to sleep.
Sometimes the baby just wants to be held and rocked in it's mothers or fathers arms.
There's a lot of things that can cause a baby to become fussy at night so check the baby and make sure they're dry, fed and then see if they want to be cuddled and held.
If the baby is fussy at night due to colic then you can give them some gripe water to help with the stomach problems which can help the baby calm down due to the colic.