In general, this can be used to find the port of any service that you might be interested in.
In my case I needed to setup a small testing scenario, involving a PC and a laptop. The PC containing an instance of SSAS that contains the data for the application.
So I needed to setup the firewall to allow the connection to SSAS from the laptop.
In order for me to do that, I needed the port number that the Analysis Services service is listening at. This can be found in two/three easy steps (should be almost the same on Windows 7 and Windows Server 2008 R2)
First you fire up your Task Manager:
From there launch the Resource Monitor and select the Network tab, then look at the TCP connections section:
or take a look at the Listening Ports section: