I agree with all the above regarding method books, solos and private lessons. I would also add the other three most important aspects of improving as a musician; listen, listen and listen... Find as many recordings, cds, YouTubes, recitals, etc. of all the euph pros and don't just casually listen to them but listen with intent. Don't be afraid to listen to musicians outside the sphere of the euphonium as well. To learn lyrical phrasing, vibrato control, etc., I listened to singers like Barbara Streisand and Andy Williams. (Back in the day) Both are masters at lyrical phrasing and "tasteful" vibrato. I would also recommend jazz trombonist Bill Watrous for the same reasons. His tone, technique etc., are second to none IMHO.
1979 Yamaha 321S Euphonium
1965 Conn 7G/6H Valve Trombone
2014 Wessex BR140 Baritone