Many textural colors and shades can be created using muted brass. Many different types of mutes were created and used during the swing era. Still in common use today are the following: cup, straight, plunger, harmon, bucket, and sometimes the hat. For the latter two (bucket and hat), you are more likely to see written into the part "play into stand", as a more convenient replacement. Have a musician friend demonstrate each of the various types of mutes and ask what to avoid when writing for them.
There are certain circumstances where mutes are essential. To help adjust balance problems, to blend better with flutes and clarinets, and to create special harmonic textures.
When writing muted parts, give the player ample time to take a mute out or put it in - especially trombonists. Mute changes should be clearly indicated in the parts - see example below. Use the term "Mute Out" not "Open", because open could have a different meaning, such as a solo section in which the repeats are open ended.