In general, the softer you notate a brass instrument to play, the less timbre-change is available. The louder, the more you have to play with. Timbre quality is generally notated as text above the staff. For example, Brassy! is a common notation, letting the player know to somewhat overblow so the bell of the instrument rings with an edginess to it. Similarly, in French Horn music the notation Bells Up is a common way to say to the horn players "I want people on the other side of the world to hear you!" Still, the options for timbre are limited. Generally speaking, the timbre is controlled by the amount of air being forced through the instrument (the dynamic marking). Slurs, dynamic markings, and articulation marks have the most impact on the sound/timbre coming out of the instrument:
> = Accent the beginning of the note
sfz = Really accent the beginning of the note (you can even exagerate this with sffz)
fp = hit the note at forte, but then back way off to piano
. = stacatto; play the note short (often about half the length written--often used simply to add separation between notes, helping accent subphrases without actually accenting notes!)
_ = legato; almost slur the note into the following note (you still tongue the next note, however) -- this does generally have the effect of making the tome more mellow
> with _ = Accent the start of the note making it a bell tone--very common in brass
There are a myriad examples of how a composer can subtly give clues to the performer on what the intended sound should be. Remember, if all else fails, you can simply write above the staff the sound you are going for (e.g., distant sounding or brassy!). I would highly recommend that you study some brass scores with a recording of it next to you as you analyze the score.