Get a pint glass, fill it halfway with Guinness and then top off with Vodka, letting the 2 mix. That's it. Start drinking.
Now some people want to layer this drink, like a Black and Tan, but you'll have to put the Guinness in first and then end up with a drink that has straight Vodka on top.
If you know someone who has compulsive obsessive disorder, challenge them to layer it but have them start with the Vodka, then try to get the Guinness to stay on top.
Variations on the Black Irishman:
Clear Black Irishman - use EverClear instead of Vodka. (aka Blackout Irishman)
Black Peppar Irishman - use Absolut Peppar Vodka
A link that mentions some "Irish" named drinks - toward the end
Some sociological "roots" on the Black Irish