How do I prepare seeds inside berries for storage/trading?
You have two options: clean the berries, or let the berries dry intact with pulp. As many berries contain chemicals that inhibit germination, their seeds will germinate more readily if the flesh is cleaned away. This is especially true for berries with hard-shelled seeds. Some berries contain soft-shelled seeds which store longer if they are not cleaned. They lose viability quickly and need to be planted soon after harvesting and cleaning. Again, you can post questions to the Growing From Seed forum for plant-specific information.
All berries, even those that have been dried with pulp for storage, are generally best cleaned before planting. If the berries are already dried, soak them overnight to soften the pulp. Before cleaning *fresh* berries, allow them to over ripen. Once the skin begins to wrinkle and the berry becomes mushy, it is ready to clean. Some berries are poisonous or contain chemicals that can irritate the skin, so it is a wise precaution to wear rubber gloves when cleaning them. Put the berries in a mesh strainer and mash them gently against the mesh while holding under running water. As the seeds are separated from the pulp, pick them out and put them on a paper towel to dry thoroughly before packaging and storing.