Filter by process/PID in Wireshark

Just in case you are looking for an alternate way and the environment you use is Windows, Microsoft's Network Monitor 3.3 is a good choice. It has the process name column. You easily add it to a filter using the context menu and apply the filter.. As usual the GUI is very intuitive...

I don't see how. The PID doesn't make it onto the wire (generally speaking), plus Wireshark allows you to look at what's on the wire - potentially all machines which are communicating over the wire. Process IDs aren't unique across different machines, anyway.

You could match the port numbers from wireshark up to port numbers from, say, netstat which will tell you the PID of a process listening on that port.