You would need to use the directions API to get the directions (part
of the output is an encoded string of the line of the route) and then
include that encoded string in the URL of your static map.
Bear in mind that the encoded string may push the length of the URL
over the limit for static maps.
http://code.google.com/apis/maps/documentation/directions/
http://code.google.com/apis/maps/documentation/staticmaps/index.html#EncodedPolylines
v1 ?? Static Maps v1 didn't support Directions directly.
You can write a server side application that gets the route from the
Directions service, extracts the polyline representing the route, and
uses it to construct a Static Map URL ready to insert in your webpage
<img> tag