The best things you can do are to be upright (yes, standing if that's comfortable, it might not be, but kneeling is great), to initiate breastfeeding right away if you're choosing to BF, have constant skin to skin contact (baby never taken away, always right on your chest), keep the room quiet, dimly lit and without everyone rushing around, and to not clamp the cord before the placenta is delivered (unless there is a medical reason to, like heavy bleeding, in which case they would encourage you to have the syntocinin injection for the placenta anyway). It's the oxytocin in our bodies that encourages the placenta to shear off the uterine wall just like it's oxytocin that encourages contractions that push your baby out. The oxytocin system works best when we're relaxed and feeling loved up with our babies close to us. Taking the baby away to be cleaned or swaddled right after birth can interfere with this as can midwives/nurses/doctors rushing around, being noisy, generally being disruptive or stressed. Just asking for some time (an hour is a good rule) to have skin to skin contact, feed and wait for the placenta, assuming everything else is fine is probably your best bet for a natural 3rd stage. Also ask everyone to back off and not disturb you while you do this.
I ended up having a managed 3rd stage, but only after an hour and 25 minutes of waiting for the placenta to come. What I think caused problems for me was that I didn't initiate BF while I was waiting and the midwives started putting lots of stress and pressure on me to deliver the placenta, even though I'd asked for time to just rest and relax. I was fine, not bleeding heavily, but frankly I think they were just in a hurry to end their shift on time (I had a home birth). They did a lot of rushing around, figeting, talking loudly, and no one helped me with latching because they were all too busy trying to rush the placenta along so they could leave. So it took a long time and I have to have the injection. No retained placenta or any real problems with it other than just taking awhile. Next time I'll ask for more privacy and make sure to get a feed in, in addition to the skin to skin I had this time, which I imagine will help a lot.
Don't worry about being upright though, really. A placenta can't rip in half just because of the weight of gravity, though pulling on the cord (a bad practice, called cord traction, that some OBs and midwives still do) sometimes can, especially if the placenta is already breaking apart. Placentas are really tough (I do placenta encapsulation so handle them often and they are incredibly strong - I have to use a lot of force with a pair of really sharp surgical scissors just to cut through one) and a retained placenta won't be caused by being upright alone, though gravity can cause the bit that had already broken apart to fall out more easily.
of which there was none..
