--Mantra is the sound-body of a god and Yantra depicts that sound-body in a diagram. Just imagine Mantra as the computer code while Yantra as the computer electronic circuit board.
Mantra = (Man = to think or meditate + Tra = is to protect; so Mantra = That which protects upon meditation)
--Yantra = instrument, engine, apparatus, amulet with mystical diagram endowed with protective occult powers. Yantra is a plate or paper on which geometric figures are drawn which concentrate the power of god.
--Tantra is a systemized way of offering worship.

Mantra are chanted according to the rules of Tantra; the vibrations gather on the surface of Yantra and bounce off on their way to the specified god. The vibrations come into contact with the god, gather power and blessings and return back to the Saadhak (the chanter of Mantra) suffuses him with divinity and confer on him supernatural powers. Thus Mantra, Tantra and Yantra are complementary to each other.

An analogy to explain Mantra and Yantra - Mantra is your name and Yantra is your body depicted on a paper as a line diagram. When you see your line diagram, you say your name; that is Mantra. Think of the deity who carries the specific Mantra and Yantra.