Paint testing is the step everyone performs and very few people perform usefully. The standard method is to brush three small patches side by side on one wall, look at them for a minute, and choose. That method reliably produces a colour that turns out to be wrong once it covers the room, and the reasons are all avoidable.
The first problem is size. A patch the size of your hand is surrounded by whatever colour is already on the wall, and the eye judges any colour relative to what is next to it. A warm white beside an old magnolia wall will look stark and blue; the same white over the whole wall will look warm. Make the sample big enough that it has its own middle. Half a metre square is a reasonable minimum.
The second problem is the surface underneath. Testing directly on a wall that is currently a strong colour means the old colour is influencing both the sample and your perception of it, and a single coat of a pale paint over a dark wall is not the colour it will be at two coats over primer. Paint onto card instead: a sheet of A3 or larger, or a piece of lining paper, given a coat of white primer first and then two proper coats of the candidate, left to dry fully. Paint changes as it dries and again as it cures, and wet paint is not evidence.
The third problem is that walls do not all face the same way. A board can be carried; a patch cannot. Once you have boards, prop each one against the wall opposite the window, then the wall beside it, then the wall the window is in, which is always the darkest surface in the room and the one people forget. Put the board flat on the floor too if you are choosing a floor finish, because horizontal surfaces receive far more light than vertical ones and read several shades lighter.
The fourth problem is time. A room is used in the morning, in the afternoon and in the evening, and a colour has to be acceptable in all three. Leave the boards up for three days and glance at them rather than staring; the colours you keep liking when you are not trying are the ones to shortlist. Deliberate staring tends to select for novelty, which is the last quality you want in a wall.
Two smaller refinements make the process more accurate. Look at the candidates against a sheet of plain white paper, which exposes undertone instantly, and look at them against the things that will actually be in the room: the floor, the largest piece of furniture, the curtains. A colour is never seen alone once it is on the wall, so there is no sense in testing it alone.
Finally, test the finish and not just the colour. The same colour in a flat matt and in an eggshell is two different results, because sheen changes how much light bounces and therefore how deep the colour looks. Flat finishes absorb light and deepen colour, hide wall imperfections and mark more easily. Eggshell and satin reflect, lighten the perceived colour, show every ripple in a bad wall and wipe clean. If a room has walls in poor condition, a flat finish will do more for it than any colour will.