Classic is not available for download; it is only playable on the website. There are, however, special downloadable "client wrappers" that provide extra features, like hacks; WoM is a good example. Google search "Wom client" and follow the directions at the WoM website. u cant. I assume that you mean Java, as minecraft classic is not something you download, so search java and download it.
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https://minecraft.net/classic/list
You can play Minecraft Classic for free from the Minecraft webpage.
No you do not need to download minecraft classic, its browser based. The full version however does involve files being stored on your PC.
There is a free version called Minecraft Classic available on the minecraft website.
You can get free Classic Minecraft from the minecraft website, and play the demo version there too for free.