A 3-way pair controls a light from two places. Power (the hot) lands on one switch's common (the dark screw); the two travelers run between the switches; the second common feeds the light. Never switch the neutral — do that and the fixture stays energized when it's "off."
Three- and four-way switches shall be wired so that all switching is done only in the ungrounded (hot) conductor.
A white/gray conductor used as a hot must be permanently re-identified (tape/marking) at each visible location. A bare white on a brass screw = the calling card of a rushed job.
A grounded (neutral) conductor shall be provided at switch locations that control lighting — new in 2011, still missed today.
Snap switches shall be connected to an EGC (the green screw bonds the metal yoke) — a fault otherwise energizes the cover plate.
A four-way goes in the middle; listed equipment installed per its instructions.
Devices: Leviton. Any hand tool shown = Klein Tools.