This is the shoe of a Speedlite 550EX with a very rudimentary connector. Yes - it's ugly. I suppose a more reliable one can be bought somewhere.

The principle is simple - just short-circuit the middle pin (the small green arrow) to the brass contacts in the slit (the large arrow). When short-circuited, the flash fires...

I am not entirely sure how long trigger pulse needs to be, but I stretched it to 50 ms with a delay unit. A simple NPN-transistor was used to give the trigger pulse - a relay would be too slow. In order to make it work, note the polarity. The middle pin must be connected to the collector and the slit contacts to the emitter.