On top of the dynamic markings, which the kind posters above have noted, many composers (including myself) will also add other notes for performers and conductors – sometimes stylistic hints that will give performers not only a clue as to how loud the piece should be played, but how the piece should flow. Useful words, from the classical word include:
cantabile – in a singing style
con moto – with motion
con brio – with vigor, brilliance, spark
con spirito – vigorously, spirited
molto – “a lot…”
grandioso – grandiose
dolce – sweetly, softly
… and so on. The composer also specifies tempo (the speed at which you play a piece) – italian words are often used for that, or metronome markings (beats per minute, according to a specific note count). Combine a few of these elements, and you can start a piece with a dynamic level at, say, pp (pianissimo, soft) with a marking for it to be played: Andante, dolce cantabile, in a sweetly singing, swaying tone, to be played at a walking pace (andante is about the speed of a leisurely walk).
You’ve set the feeling for the whole piece, right there.