An opera orchestra is essentially a symphony orchestra with some modifications. There are three major sections: the strings, the winds, and the percussion; plus some add-ons.
The string section includes the violins, altos, cellos, and doublebasses. The winds section consists of the brass (the trumpets, trombones, tuba, the French horn), the woodwinds (clarinets, oboes, and the English horn), and the flutes. The percussion section includes the drums, bells, triangle, and cymbals).
It is customary for an opera orchestra to feature at least one harp.
It is really up to the composer to include any additional instruments (a piano or a saxophone, for instance).
During the Baroque period, orchestras were small. Kristof Gluck, Wolfgang Mozart, and Ludwig van Beethoven, among others, contributed to the expansion of the standard symphony orchestra. Large opera orchestras came into existence with the advent of the Grand Opera period.
Richard Wagner almost doubled the size of the orchestra for his operas. In Bayreuth, the opera theatre whose construction was conducted under Wagner’s direct supervision, features an orchestra pit hidden completely under the stage (so as not to distract the audience). This, among other things, contributed to the size of Wagner’s orchestra.
The conductor’s job is to keep all that wealth of music together (see my article on conductors).
Each opera company has its own orchestra. While different singers (and conductors) can sign on for different performances, the members of an opera orchestra usually stay together for the entire season, performing all of the company’s repertoire, night after night.
Even though modern technology has created many new ways of delivering music to the listener, and many new instruments have been invented over the past century, nothing matches an orchestra when it comes to depth, expressiveness, and passion. Some of today’s movies, for instance, in which music is called upon to enhance the psychological effect (including action flicks, comedies, and psychological drama) hire composers to write orchestral scores to fill the soundtrack.