Fill a highball glass with ice.
Add the Irish whiskey and lime juice.
Top with cold ginger ale.
Stir once, gently.
Garnish with a lime wedge.
A Buck is any spirit with citrus and ginger — the Mamie Taylor and the Moscow Mule are both Bucks wearing better names. Irish whiskey's lack of aggression is the point here: use ginger ale rather than ginger beer or the spirit disappears entirely.
My Bar Shelf reads your shelf and shows you every cocktail you can make from what you already own, including Irish Buck.