I’m almost totally ignorant about classical music as I’ve only become really interested in it over the past couple of months. It seems to me though that many pieces would lose much of their impact if not for the variations in volume throughout the piece.
How is this translated onto sheet music?
Here’s wikipedia’s page that describes the notation for dynamics and relative loudness.
Dynamic levels are notated on the sheet music. Piano (soft,) forte (loud,) pianissimo (very soft,) fortissimo (very loud,) and so on. Crescendos are also written as part of the score, and individual notes are emphasized with markings. On top of all that, the visual direction of the conductor leads the performers.
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.
Thanks for that link and for the answers from everyone else. I am even more awed at the complexity.
It’s also important to note that the various volume levels are not an arbitrary, measurable designation: one conductor’s “let’s play really loud here where it says Forte” is often another conductor’s “shoot, we can play louder than that”.
The whole field of musical interpretation of the composer’s dynamics markings is where you can get into really vicious, caviar-slinging arguments over So-and-so’s handling of the Such-and-such Symphony, etc. Much fun. 
You should learn to play a musical instrument, PM. Even if it’s just a beginner course in piano, it’ll give you much insight into the exotic world of Classical Music.
Trivia: Condoleeza Rice’s first name comes from the music notation Con dolcissima, “with great sweetness”.
Except Percy Grainger, who wrote things like “louden hugely”.
I’ve played Grainger in the past, and I was always amused by these markings too. However, there’s a bit of a sinister side to them:
From the Wikipedia article on Percy.
The thought has crossed my mind more than once lately. Piano is definitely top of the list.
Trivia, part deux: The cannonfire in the 1812 Overture is annotated in the score: ffff, which I can only assume translates as “just really, ungodly freaking loud.”
That’s the classical equivalent of “It goes to 11.”
In addition to notations such as pp and ff, there are also a few denotations of expression, such as staccato, legato, marcato, spiccato, and pizzicato. Since it is very difficult (on some instruments) to play staccato and pianissimo, for instance, such expressions tend usually to suggest a given level of volume.
Some instruments have no variation in volume whatsoever: a harpsichord, for instance, plucks the strings at a constant volume regardless of the musician’s intent. Making a harpsichord louder employs a technique that is technically called “playing a bunch more notes and stuff, like, at the same time.”
I know everybody knows this but for those that may not… the full name of the instrument known as the piano is really the pianoforte which literally means soft-loud. (Actually, the full name is the Italian translation for ‘Harpsichord with soft and loud’).
Why, because up until that time, keyboard instruments plucked the strings and the loudness could not be varied.
In that case, I’ve played pieces which go up to 14 
Well I’ll be damned. I’ve played things by Grainger and have ALSO noted the somewhat bizzare markings. However I just passed it off as him describing the dynamics etc. in his native language.
Crescendo poco a poco became getting louder little by little. I got a good chuckle.
AIUI, being a fan of Elgar’s The Dream of Gerontius but not having played or sung it, there is a single chord where the Soul stands before God for an instant, and the composer directs that “each player should exert his utmost”. Most brass players, at least, would take this as a challenge.
At the other end of the scale, I’ve seen pppp in Berlioz’s The Shepherds’ Farewell, third verse, and the conductor’s comment was “He really means it this time”.
Bloody brass players.
The Italian instruction possibile is not unknown in conjunction with dynamics, particularly cresc. and forte, as well as piano.
Then there’s a whole load of other markings which, while not simply being about dynamic level, have some crossover: it doesn’t take much Italian to work out what is mean by something like molto feroce.
Mostly it’s the trombonists you have to watch out for. We trumpeters are quite refined really.
Gustav Holst specified the volume of the women’s choir in the “Neptune” movement of the Planets suite. He said they were…