One way is to vertex snap the pivot point to the bottom of the object (hold d and v and MMB click on a bottom vertex), then x snap the object to the grid (aka floor). This is a bit of a workaround and doesn't work for every situation.
In the Maya Bonus Tools, I believe there is a layout tool for dropping things to the floor.
In many cases, with complex objects, it's as simple and mundane as eyeballing it.