Classical composers are those who write classical music. Some music is written for full orchestra without a soloist. Some is written for a soloist to perform with an orchestra to back the soloist. Others are written for smaller amounts of musicians, like chamber music or music for a duet, trio, quartet, quintet and more.
Most composers were employed by noblemen to write music for them.
Ludwig van Beethoven was one of the first composers to earn a living by selling his work to publishers.
Most composers of classical music started out as musicians and as time went were either were taught to compose or like Wolfgang Amadeus Mozart they had a natural talent for it and started composing at very young ages.
Music has been composed ever since the beginning of time but it wasn't until the eleventh century that classical music was composed. Classical Music has been broken in to periods since then; the Renaissance, Baroque, Classical, Romantic, and 20th Century.