1. The object is at rest. This might seem obvious, but if an object isn't moving, its velocity is zero, and since it's not changing, it's constant.
2. The object is moving in a straight line at a constant speed. For velocity to be constant, both speed and direction must be unchanging. So, a car traveling at 60 mph due north has constant velocity.
Key Point: Constant velocity means both constant speed *and* constant direction.