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One way to describe the location of an object in the sky is by using altazimuth cooordinates, also know as horizon coordinates. These coordinates are always relative to a specific observer's location.
It takes two numbers to describe a location in horizon coordinates.
The altitude or elevation is the height of the object above the idealized horizon (or where the horizon would be if the local terrain were flat). An elevation of π/2 radians is straight up, also known as the zenith.
In practice, some objects at negative altitudes are visible: from South Baldy at 10,000' in the Magdalenas, it is possible to see a bit below the horizon in some directions.
The azimuth is the equivalent of the compass direction. An object due north of the observer is considered azimuth zero, and values increase clockwise in the order N→E→S→W→N. In radians, the values are in the range [0,2π).