Create a BroadcastReceiver listening for WifiManager.NETWORK_STATE_CHANGED_ACTION, grab the SSID from the intent extra WifiManager.EXTRA_BSSID inside onReceive.
If your SSID processing work is expensive, offload it to a service (see the docs for BroadcastReceiver.onReceive).
Your AndroidManifest.xml should look something like:
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
...>
<!-- Permission to listen for network changes -->
<uses-permission android:name="android.permission.ACCESS_NETWORK_STATE"/>
<application
...>
<receiver android:name=".YourBroadcastReceiver" >
<intent-filter>
<action android:name="android.net.wifi.STATE_CHANGE" />
</intent-filter>
</receiver>
</application>
</manifest>