How do I tell the accuracy of my position?

The HDOP value can be used to determine the accuracy of the GPS position.  Lower is better.

The HDOP can be seen when using gpsmon. The image below has HDOP highlighted;gpsmon HDOP
The HDOP can also be found in the GSA sentence.  Below it is shown as 1.3;

$GPGSA,A,3,04,05,,09,12,,,24,,,,,2.5,1.3,2.1*39

A HDOP value of 1 or below would give you an accuracy of about 2.5m.

See here for more information.