It really depends on your comfort level and setup. At three months it's not uncommon for the baby to share a room with the parents in a bassinet. Three month olds don't really do much and you want to work on the baby sleeping during the night, so you'd want to hold them for a bit until they get settled then lay them down to let them fall asleep in the bed of choice. Depending on the baby this could take some coaxing, cuddling, etc. if they're in their own nursery and you have a monitor or something you can put them down, go back to bed, and either try and get back to sleep or watch them for a bit. But yes, you would hang out with them for a bit to get them back to sleep. It is super peaceful holding a sleepy baby.

nah, you just spend a while burping them and then rock them in the colic position until they fall asleep.

Source : I am a Creampie aficionado.

Lay next to the crib and go to sleep to show how it's done.