Note: tcpdump requires root privileges, so you'll have to root your phone if not done already. Here's an ARM binary of tcpdump (this works for my Samsung Captivate). If you prefer to build your own binary, instructions are here (yes, you'd likely need to cross compile).
Also, check out Shark For Root (an Android packet capture tool based on tcpdump).
I don't believe tcpdump can monitor traffic by specific process ID. The strace method that Chris Stratton refers to seems like more effort than its worth. It would be simpler to monitor specific IPs and ports used by the target process. If that info isn't known, capture all traffic during a period of process activity and then sift through the resulting pcap with Wireshark.