The Euphonium went through a number of changes before becoming what it is today. First came the Serpent, followed by the Ophicleide. In 1823, William Wieprecht made a piston valved instrument called Tenorbasshorn, in 1838 Carl Moritz of Berlin made a similar instrument called a tenor tuba, and finally in 1843, a person named Sommer of Weimar designed and named a piston valved, tenor instrument called a "euphonion", which most people today believe is the ancestor of the modern Euphonium. While this instrument is not very popular in the orchestra, it is an essential part of modern band ensembles. It is used in a variety of concert bands, wind ensembles, and an essential part of the British Brass Band. Euphoniums come in either 3 valve or 4 valve set ups (piston valves), with the 4 valve set ups being either compensating or non-compensating.
Like trombone, the Euphonium is in the key of Bb, but reads concert pitched music. Because of this, it is a non-transposing instrument.
More here
The Euphonium is played by buzzing lips together through the mouthpiece. Using your left hand to press down on the valves, you hook your thumb underneath the arc for support and place your index, middle, and 'ring', finger one the top of the valves. your left arm wraps around the instrument to support it and hold it up. If the instrument has a 4th valve on top, it is played with the pinky finger. If the 4th valve is on the side, it is played with the left index finger. Pressing down different valve combinations, along with your embouchure, change the notes.
Demondrae Thurman is a highly regarded Euphonium player in the music community. He has performed with various groups such as the New York Philharmonic, Atlanta Symphony, Sarasota Orchestra, North Carolina Symphony, Eastern Music Festival Orchestra, Oregon Symphony, and the Philadelphia Orchestra. He has been invited as a guest for the highest level low brass festivals like the International Tuba/Euphonium Conference, U.S. Army Band Tuba and Euphonium Conference and the Leonard Falcone Competition. Thurman is also the lead Euphonium of the very popular Sotto Voce Quartet, which tours extensively. He currently teaches at Indiana University as the Professor of Euphonium.
More here.