How can i export directions?

Just send the directions to someone else, enter the details and copy the full URL that you see in your browser's addres bar, for example:

http://www.openstreetmap.org/directions?engine=osrm_car&route=37.77928%2C-122.41927%3B37.34385%2C-121.88313#map=10/37.5625/-122.1501

To send the text of the directions, just copy the text from "Directions" to the bottom of the page and paste it into e.g. a mail message.

... or if that isn't what you want to do, could you perhaps describe what you'd like to be able to do (or even better, describe it over at Github in an issue added to describe a possible enhancement)?

http://project-osrm.org/ is an excellent router and you can generate a link or export a gpx of the route. It is also useful for testing if mapping and the routing are correct, such turn restrictions and node connections, but if you have just done some edits they won't show for a while.

Have a look at Routing -> Online Routing to find some OSM based websites where some of them can export the routing als GPX or KML file.

If you are using the routing from the osm page, after drawing the route, if you select the 'Directions courtesy of OSRM' link and copy the start and end coordinates into it, you will get a gpx link. I expect that function will be on the osm page in time.