Protocols in the lower layers of the OSI Model as shown in the link below, have very well defined structures.
TCP for example has certain flags which are set depending on the point in the three way handshake. Applications such as nmap take advantage of this to perform SYN scans, RST scans, etc.
You can modify an IP header to spoof the source IP address of a packet.
You can give a packet an invalid checksum so see how a receiving device handles it.
You can say the size of the packet is really large, but only send them a small amount of data, or vice versa.
You can even fuzz these structures to find weaknesses in the layers themselves that you might be able to take advantage of.
There's a lot to learn by learning networking as well.
Reference:
http://f.tqn.com/y/compnetworking/1/S/g/basics_osimodel.jpg