For the first 5-6 weeks, really all your baby will want to do is eat, sleep and poop. Mostly eat. You will feel like he is attached to you 24 hours a day. He is growing a lot and he is building your supply. Just keep nursing him whenever he wants for as long as he wants, even if he just ate 30 minutes ago.
At the major growth spurts too you will notice an increase in feeds (3 weeks, 6 weeks, 3 months, 6 months) and also at night baby's will often do what is called "cluster feeding" where they will pretty much nurse non stop for 3-4 hours. they are usually stocking up for a little bit longer nighttime stretch.
With my first son I didn't know any of this. He was nursing constantly at night, from about 7pm to 11pm and I was in tears thinking I wasn't making enough milk, that I was doing something wrong, that I would never be able to put him down. So take comfort in knowing that it's normal and your baby is doing wonderfully and doing exactly what he should be doing; building his bond with you and building your milk supply so he can grow big and healthy.
After you hit 6 months, you should notice a change in the nursing habits. He will get into a more regular routine of nursing every 2-4 hours and going a longer stretch at night (if you're lucky, not all moms get that). Except of course at the growth spurts (sometimes you get one at 4 months too, I know I did with my first) when he will go back to nursing constantly. But once you hit 6 weeks, it will all get so much easier!
Congrats momma, you are doing awesome!