Little thought is often given to the placenta, unless it is going to be prepared for ingestion. If this is the case, the placenta will require attention and care to ensure it is suitable for ingestion. As soon as the decision is made to utilize the placenta for postpartum recovery, it becomes a food item and must be treated as such.
After birth, the placenta should be placed in a food safe container. If you're birthing in the hospital, they will give you a special container for it. If you're birthing at home, you should have either a special bowl or several gallon zip lock bags set aside for the placenta.
I've had placentas given to me to prepare wrapped in towels or chux pads. This is not an appropriate container for the placenta.
After birth, the placenta needs to be refrigerated as soon as possible. If you plan to birth in the hospital, bring a small cooler with you and have the nurses put ice in it once the placenta is born. The placenta can stay on ice in the cooler for up to 12 hours, but the sooner it gets in the fridge, the better. If you choose to birth at home, put the placenta in the fridge as soon as possible.
The preparation process of the placenta should ideally begin within the first 24 hours after the placenta is birthed. If the process is begun within 48-72 hours after birth, that is still okay, but the potency of the capsules may be lessened. I recommend that if the placenta preparation process cannot begin within 72 hours, then the placenta should be frozen to retain maximum freshness and can be thawed before the process begins.
You're placenta encapsulation specialist should give you any additional information specific to your situation to ensure your placenta remains edible.
For a great article on the subject, visit http://placentabenefits.info/MWT_article.asp.