they may offer you the depo shot in the hospital before you go home and then they'll get into birth control more extensively at you 6 week postpartum visit

I got the iud after 4 weeks.

usually the Dr will talk to you at your 6 week post check up.

I had the depo shot the day after I had my oldest daughter and they did it right at the hospital before I went home, so as soon as after birth I presume :)