The primary interface between you and the packet is PacketContainer. It contains a set of StructureModifiers that allow you to modify the packet. See the JavaDoc for a list of supported modifiers. Modifiers are based on the NMS representation of a packet, NOT the wiki representation. They're generally equivalent, but the wiki shows the serialized form. Your best bet for determining the NMS representation of a packet is to search for the decompiled source file in your BuildTools work directory.
StructureModifier
JavaDoc: StructureModifier.java
StructureModifiers allow you to read from and write to a packet. Depending on how you feel about optionals, you can use modifier.optionRead(index) or modifier.readSafely(index) to read data from a packet. You can then write with modifier.writeSafely(index, value)