Professional composers often have a degree or qualification in music, but people with other degrees and non-graduates can also become musicians if their ability is of a sufficiently high standard.
Entry for orchestras and opera houses is through an audition followed by a trial period - this is not the same as a probationary period and it cannot be assumed that a permanent contract will follow.
A degree in music will give you the opportunity to develop your performance skills whilst at university/conservatoire, although some music degree courses may concentrate more on theory than practical playing - courses run by conservatoires may be more appropriate for performance/composition.
Postgraduate courses in performance can help you develop performance skills and build a network of contacts - personal references are extremely important for getting work in the music field.
Musical directors will be looking for people with considerable experience, so take any opportunities to gain experience. Seek advice from musicians already working in your area and ask for introductions.
It is advisable to write speculatively to the orchestral manager by name with a CV and introductory letter to obtain freelance work. Orchestras keep lists of people whom they contact for freelance work as required. Entry to full-time posts is very competitive and you will probably need to build a musical career incorporating performance work in a number of different settings and groups, teaching and arranging music.
Many people start their careers by gaining experience on a freelance basis whilst teaching music.