Study Music Theory. Music theory will improve a musician's ability to analyze and understand a musical work. By learning about key signatures, chord progressions and form in music a greater understanding of the music will begin to develop. A good rule is to study for 15 to 30 minutes every day. Don't move on to the next topic until you have mastered the current one.
Determine the techniques that are important to learn on the instrument of choice. For example, trumpet players should set goals to improve their tonguing speed and range, string players should increase their bow technique, vocalists must concentrate on their breathing and woodwinds should practice passages that go over "the break" in their instrument. Study privately with a qualified instructor to improve technique and get valuable guidance in this area.
Study the instrument's repertoire. Each instrument has its own set of classical repertoire. Determining what pieces are basic knowledge for a particular instrument choice and memorize each piece. Contact a local professor or instrumental instructor to obtain opinions on what is possible. The repertoire will help to build technique and to increase overall ability. Try to memorize at least one piece a month.
Work towards playing in live performances. In a performance, all the hard work comes together and forms into a final product. The performance allows an instrumentalist to test his abilities and nerves to give the audience a perfected product. While mistakes happen in a performance, proper preparation will help minimize those mistakes. Most importantly, in the performance, it isn't how perfectly you perform the piece, but how musically you perform it. Several prominent musicians have been known to make mistakes in performances, but their musicianship is on such a high level those mistakes are forgiven.