The one rule everything else uses: reduction
Numerology works in single digits, so every total is reduced by adding its digits until one digit remains. 47 becomes 4 + 7 = 11, and 11 becomes 1 + 1 = 2.
With one exception. 11, 22 and 33 are master numbers and are not reduced — a total of 11 stays 11. This single exception is the source of most disagreements between numerology sites, because whether you check for it before or after combining components changes the answer.
From the date: Life Path
Reduce the day, the month and the year separately, then add those three results and reduce once more. Take 29 February 1980: the day 29 becomes 11 and stops there because 11 is a master number; the month is 2; the year 1980 becomes 18 and then 9. Adding 11 + 2 + 9 gives 22 — itself a master number, so the Life Path is 22.
The alternative method — summing all eight digits at once — gives 4 for that date. Both methods are in circulation and they disagree on about one birth date in eight. The component method above is the standard one, and it is the only one that can see a master number living inside a single component.
From the date: Birthday, Mulank and Bhagyank
The Birthday number is simply the day of the month, un-reduced: born on the 23rd, your birthday number is 23. Indian numerology reduces it instead and calls the result the Mulank — 2 + 3 = 5.
The Bhagyank is every digit of the full date reduced to a single digit, with no master-number exception. For 23-04-1990: 2+3+0+4+1+9+9+0 = 28, then 2+8 = 10, then 1+0 = 1.
From the name: Destiny, Soul Urge and Personality
Give each letter a value — A=1, B=2, up to I=9, then J starts again at 1 — and the three name numbers are three different subsets of the same letters.
All the letters give the Destiny (or Expression) number. The vowels alone give the Soul Urge. The consonants alone give the Personality. Take AARAV: A=1, A=1, R=9, A=1, V=4. All five letters sum to 16 → 7, the Destiny. The vowels A, A, A sum to 3, the Soul Urge. The consonants R and V sum to 13 → 4, the Personality.
The personal year
This is the only number that changes. Add your birth month, your birth day and the current calendar year, each reduced, then reduce the total. It rolls over on 1 January, not on your birthday — which surprises people, and is the standard.
What is not calculated
Everything after the arithmetic is interpretation. The number is a fact; that a 7 is drawn to research is what the tradition holds. Any page that blurs those two things — presenting a reading with the same certainty as the sum that produced it — is doing something the arithmetic does not license.