Six numbers describe what your character is physically and mentally capable of. Everything else on the sheet is a modifier applied to a roll made with one of them, so this is the step that decides what your character is good at.
What matters at the table is not the score but its modifier — the number you actually add to an ability check, a saving throw or an attack. Scores go up in steps of one; modifiers go up in steps of two. An odd score buys nothing on its own, which is the single most useful fact on this page.
Point buy is the default, and the only one that guarantees every character at the table starts equally capable. You have 27 points, every ability starts at 8, and you raise them by paying from this table:
| Score | Cost |
|---|---|
| 8 | 0 |
| 9 | 1 |
| 10 | 2 |
| 11 | 3 |
| 12 | 4 |
| 13 | 5 |
| 14 | 7 |
| 15 | 9 |
No score can go below 8 or above 15 at this stage. The costs are deliberately uneven at the top — going from 13 to 14 costs 2 points, and 14 to 15 costs 2 more — so a single maximised ability is paid for by two mediocre ones.
The standard array is point buy with the decision already made for you: 15, 14, 13, 12, 10, 8, assigned to the six abilities in whatever order you like. It costs nothing to think about and lands in the same place as a sensible point buy.
Rolling is the traditional method: roll four d6, drop the lowest, six times. It can produce a character stronger than either method above, and it can produce one meaningfully weaker. Ask your DM before assuming the table uses it, because it is the one method where two characters can start unequal.
Your background raises three of your abilities, after the method above rather than before it. You either add +2 to one and +1 to another, or +1 to three.
Do this in the right order and it pays for itself: point buy stops at 15, so a 15 plus a background's +2 is a 17 — a number the method alone cannot reach, and the difference between a +2 and a +3 modifier on everything your class does. Choosing the background first and squeezing the points around it is how people end up one point short of an even number.
The six are covered in full on The Six Abilities. For this step, the short version is that your class names one primary ability, your two saving throw proficiencies come from that class, and Constitution quietly matters to everyone, because it raises every Hit Point total you will ever roll.
If you would rather see the arithmetic than do it, the Ability Score Calculator runs all three methods and applies your background's increases for you.