A birth chart is a circular diagram of where celestial bodies stood at a particular moment as seen from a particular place. Its construction is calculation, and interpretation is a separate stage.
Three inputs determine the whole diagram
Date, exact time and geographic location are all required, and each affects the result differently.
Date establishes where the planets are in their orbits, and small errors in date produce small changes for slow bodies and larger ones for the Moon.
Time and place together establish which part of the sky was rising, and here small errors matter a great deal, since the rising point moves through the full circle in a day.
Positions come from astronomical tables
Planetary positions are taken from ephemerides, the same computed tables used in astronomy, and the underlying figures are not in dispute.
Historically these were laborious to produce and were among the most demanding calculations any society performed, which is why astronomy and calculation developed alongside each other.
Software has removed the arithmetic entirely, which changed the profession considerably, since accurate chart production was formerly a skill in itself.
Houses divide the sky and the methods disagree
The chart is divided into twelve sectors representing areas of life, and there are numerous competing systems for drawing those divisions.
The systems produce noticeably different charts for the same birth, particularly at high latitudes where some methods become distorted or unusable.
Practitioners choose a system by tradition or preference, and the disagreement is long-standing and unresolved within the field itself.
Aspects are angular relationships
Angles between bodies, measured around the circle, are treated as significant when they fall near particular values such as ninety or one hundred and twenty degrees.
How much deviation is allowed before an angle stops counting is another point of variation, and different schools use different tolerances.
These are geometric facts about the diagram, and their significance is the interpretive layer laid over them rather than part of the calculation.
The zodiac used is itself a choice
Western practice generally measures the twelve divisions from the equinox point, while Indian practice measures them against fixed stars, and the two frames have drifted apart by roughly a sign over the centuries.
The result is that the same birth yields different sign placements depending on which convention the practitioner uses, which regularly surprises people who encounter both systems for the first time.
Practitioners in each tradition have reasoned defences of their convention, and the divergence is a well-known feature rather than an error in either system.