My favorite era of classical music is the Late Classical through Early-Romantic time period (approximately composers born between 1750-1800). Mozart and Beethoven were both born during this time. You'll also find Niccolo Paganini, Franz Schubert and other here. Orchestras have evolved in size and composition over time. But I'll focus on one of the more simple orchestral structures, the Classical Orchestra.
Step One: Write some music; Directing traffic
You need a composer and a conductor (sometimes the same person). The composer writes the music. The conductor sets tempo, helps shape the music, gives cues and makes sure everyone is on the same page. The conductor is usually positioned front and center, back to the audience, waving his hands about. (However, a conductor is not necessary. Earlier Baroque music and smaller orchestras will sometime have the principle violinist act as the conductor).
Step Two: Get Some Strings
The strings are typically the largest part of the orchestra. This section is made up of: Violins (1st and 2nd); Violas; Cellos (Violoncellos); and Double Basses. Size varies. Some pieces call for a handful of strings, other call for 14 violins (each), 12 violas and cellos (each), and 10 basses. Their organization typically fans from violins on the left to basses on the right of the conductor (see image below).
Step Three: Get Some Woodwinds
Components: Flutes, Oboes, Clarinets and Bassoons. Usually two of each; some pieces call for more. The clarinet is usually divided into a B-flat and an A Clarinet.
Step Four: Get Some Horns
Components: Horns, Trumpets and Trombones. Usually two trumpets and trombones, four horns. Sometimes you will see a tuba.
Step Five: Get some Percussion
Components: Timpani, for sure. The Percussion section has really grown over time, now sometimes including all sorts of drum, triangle, cymbals, glockenspiel, xylophone, chimes, and so on.
Step Six: Organize everyone
The composer is front and center. The strings are up front, shadowed by the woodwinds in the middle and horns on the outskirts. The booming percussion is found in the back.
Orchestras differ in size, depending on the piece, its era and whether or not it is accompanied by a chorus and soloist or accompanying a performance. The orchestra at times will be found submerged below the stage during an opera. There is no golden rule when it comes to orchestras and their arrangement and location. Hopefully this short introduction is useful. I'm planning on diving into specific instruments, their sounds and helping you (and myself) improve our abilities to hear music.