Brace yourself. You will be spending much more than expected to buy things you never even thought of. Start planning financially for having a baby as soon as you can - before conception if possible.
Set aside as much as you can every month in a savings account. The actual event of birth can be expensive as well as all the first time purchases you'll make. Don't forget to save some money for your maternity or paternity leave. This is usually unpaid time off work.
How much do you need? As much as you can save. Any funds left over make a great starter for a college fund. If you've amassed a considerable amount well before the due date, you can invest in a short-term CD or other insured investment. But don't tie up your entire fund in investments. Babies will not sign contracts and they have not agreed to your schedule.
Have a brainstorming session with an experienced parent to figure out all the things you need to purchase before the delivery. It will be extremely helpful to have most of what you need before the baby is born. Your spare shopping time after birth is reduced drastically. If you need to shop after the baby is born, try the Internet. Nobody on the Internet cares how loud your baby is crying, what you are wearing or what time it is when your baby gives you a free moment to shop.
Here's a starter list for your brainstorming session. This is far from a complete list, but it will help get you thinking.