Hi, jrramsey.
In the Applications > Utilities folder, launch Network Utility and select the Info tab. Note the entry in the Link Speed field.
Your AirPort Express should have also come with AirPort Client Monitor (ACM). This will show you a graph of link speed, i.e. the Transmit Rate, in real time, as well as signal-to-noise data.
You can also download ACM and AirPort Admin Utility by clicking the "AirPort Management Tools" link in the right margin of the
AirPort Support Page.