Practice slowly
The cellist Tina Guo sums it up in a single line: speed is a by-product of accuracy, not the other way around. Why that holds for far more than music.
Anyone learning an instrument wants to play fast. That is the temptation. You hear the piece as it sounds in your head, up to tempo, and you try to get there at once. The result is almost always a hurried mess of half-mistakes.
The cellist Tina Guo, known for her film work, sums up the counter-move in one line. Practise slowly. Speed is a by-product of accuracy, not the other way around. You do not chase tempo. You build precision, slowly, until every note is right. Then the speed comes on its own, because your fingers by now know exactly where they need to be.
A principle that holds everywhere
This is not musical wisdom alone. It is one of the most reliable principles of any craft. A sauce you whisk too fast splits. A text you write too fast misses half. A decision you rush costs you later the time you thought you saved.
Practising slowly is a form of patience most people have unlearned. We want the result without the slowness that makes it. But the slowness is the work. Whoever learns to do it precisely, in the end does it fast too. The other way round never works.