There are plenty of websites that provide all kinds of songs and music for free, including free online classical music. One can easily find several of such websites by using a search engine like Google. By searching with a simple keyword like "free music download," one can access a number of websites that provide a gold mine of songs and other kinds of music.
Each website works in different way. Some websites allow the users to download a particular music files to the computer of the user. The file stays in the computer of the user. This activity sometimes violates copyright issues. So, a majority of websites allow the user to play and hear the music. The user will need continuous internet connection. Once the internet connection is disrupted, the playing of the music will stop.
Another source of free online classical music is web radios. There are a good number of online radio stations. Some of which are free to use. Some radio stations give prominence to classical music. The advantage of radio stations is that the listeners will get a chance to enrich their knowledge about the music and a golden opportunity to hear previously unheard music.