According to legend, the simplistic, wafting tones of the "Taps" melody played at funeral marches is a tradition that began during the Civil War, when a fallen soldier and beginning trumpet player was honored with the playing of piece of sheet music that was found in his pocket: a short, four-note melody. Though the truth of this story is debatable, it's based in the idea that the "Taps" melody could easily be a pedagogical study for a beginning brass player. Since it is based on the intervals between the natural acoustic partials, "Taps" can also be played on the trombone.
Lock your slide in first position, or simply hold it there. You will not need to move it in order to play "Taps."
Stand or sit up with an upright, relaxed posture, and bring the trombone up until the mouthpiece meets your mouth. Don't allow your neck to bend forward, as this will constrict your air supply.
Learn to make sound on the trombone. Buzz your lips by pressing them together and blowing (like blowing a raspberry, but keep your tongue in your mouth). Keep your lips pressed around the contours of your teeth rather than allowing your cheeks to puff.
Practice hitting different pitch partials, and learn to move between them. Partials are different notes that you can play without moving the slide. Adjust the tension in your lips, and blow faster and slower speeds of air. Faster air and higher muscle tension will create higher pitches. You'll know when you're doing this right because it will feel like "shelves" of sound that pop into place.
Play an "F" on the piano, pitch pipe or tuner, then match this pitch on the trombone. (It will most likely be the second-lowest note you can play.) This is your starting pitch for "Taps."
Start the taps melody on a repeated "F," and play the melody you know by moving up in the partials. The other three notes you need for this tune are B flat, D and a high F (you'll have to work very hard for this last note if you're new to playing the trombone). Play these pitches on your piano in order to make sure you're matching them correctly.