Well it depends. It is also a matter of preference. There are other deciding factors such as age, size and health concerns.
My personal experience, I offered my babies the pacifier in the hospital. This was used as a soothing mechanism when they just needed to suck. Babies have a strong urge to suck. They even suck on their fingers while in the womb. I found it helpful to calm them down when they were fussy. However I did wean them from the pacifier as soon as they were cutting teeth or eating three meals a day. Again this was how I did it.
When doing your research you will find other experts will want you to wait to offer the pacifier after your baby has learned to properly latch on to your breast when breastfeeding. The concern is nipple confusion. Most pacifiers are narrow and do not mimic the shape of your breast. Therefore causing your baby to reject the breast when time to nurse. This is also common when offering your baby a bottle before learning to nurse properly.
I do not agree with placing an array of pacifiers in the crib with the baby during sleep time. I have found working with numerous babies, some have been know to toss them all out of the crib. You then have to enter the room to put them all back in. I do like the "Wubbanubs". They have a soft animal safely
attached at the end of the pacifier. This allows baby to reach for the pacifier in the middle of the night and it is big enough for them to hold on to.
When to take the pacifier away?
It is important to wean your baby from the pacifier as soon as they begin to cut teeth. It can be a choking hazard if baby bites off the end of the pacifier. Most pacifiers are pretty strong but still can become a safety concern. Parents like the quiet that a pacifier can bring to a fussy child. It is a tool to soothe a fussy baby. As your baby starts to grow explore other option to quiet and soothe your baby. Waiting too long to take the pacifier away can cause damage to a child's teeth. Allowing them to self soothe using their hands can be a great alternative.