Many attempts have been made to describe Discordianism — and many attempts have failed.
Discordianism is a philosophy. Some have described it as "like Taoism, but funnier." Some people think that Discordians take serious things humorously. That is not quite true; rather, we take humorous things seriously.
Discordianism has a lot to do with Order and Disorder (which is what Chaos uses to manifest itself onto the material plane). The two are considered equals, more or less. Discordianism isn't about anarchy, the downfall of government, and breaking stuff (of course, it isn't NOT about those things, either). It's about creativity, and that takes both Order and Disorder.
One camp of Discordians believes there is enough order in the world, and so dedicate themselves to being fonts of disorder, thus evening up the overall balance. Another camp takes things more personally, and so looks to strike a balance between order and disorder within the individual. They're both right.
Some religions require you to study a dusty old book written centuries ago by a "prophet," and you cannot deviate from its teachings, or question its validity. In Discordianism, not only are we not required to believe anything we read, but we can write our own holy books.
Some religions give you a detailed list of what you can or cannot do. Discordianism allows you to do whatever you want to do (but remember, Eris doesn't like an asshole — if someone kicks your ass for being a first-class bastard, don't blame Her).
Some religions require their clergy wear special clothing to "clerge." Discordians don't have that problem and can wear whatever we feel like.
Some religions speak of love, peace, and understanding, but actually create chaos, confusion, and disorder. Discordians speak of chaos, confusion, and disorder, but actually create peace, love, and understanding.
Some religions require their clergy to make a vow of poverty and chastity. We Discordians tend to laugh at that idea until we pass out.
Some religions require you to sit silently for hours, often in very uncomfortable positions, to attain "enlightenment." We Discordians don't have the time for things like that — we've got shit to do.