Movement in Shenmue falls generally falls into either the "Free Quest" or "Free Battle" mode, although there are some other specific controls.
Free Quest
Holding the "Zoom" trigger moves the camera into a first-person view, which can be controlled using either the D-Pad or Analog stick. This allows Ryo to "lock on" to items of interest, so you can pick up or otherwise interact with the item.
Free Battle
There are dozens of moves that Ryo can performed - see the Move Scroll for a complete run-down. Some moves cannot be performed before they are "learned" in-game - either taught to Ryo by other characters, or when you find or buy a Move Scroll.
QTE
Quick Time Events' occur regularly in Shenmue, and require you to press buttons following on-screen prompts. Missing one or more of these prompts can cause Ryo to fail the QTE, and usually means you'll have to repeat the event. This Walkthrough will attempt to detail all QTE movements.
Other Controls
Forklift
R accelerates, L brakes and reverses, and either 
or Analogue stick can be used to steer. Raise and lower the forks with A. A map of the current job can be opened with X, the inventory can be opened as normal with Y and you can beep the horn with 
.
Motorcycle
Accelerate with R, brake with L. The bike can be steered with either D-pad or Analogue stick.
Arcade Games
See the Arcade Games section for full details.