Ecclesiastes gets the ball rolling by identifying himself as "the Teacher" (Koheleth or "Gatherer"), and says he was the son of King David. So, he's got some serious authority right off the bat.
He begins his actual teaching by saying "Vanity of vanities! All is vanity!" (Everything is just "mere breath.") He then gives examples of this, discussing how everything in nature keeps repeating itself. The sun goes up and comes down, and then does it all over again. (Hooray.) The wind just keeps blowing circles around the earth, and water keeps running into the sea.
He goes on to say that everything that has happened will happen again, and everything that is going to happen has already happened: "There is nothing new under the sun" (1:9).
Ecclesiastes goes on to say that nothing that has happened will be remembered forever. Eventually, everything is totally forgotten.
The Teacher says a bit more about himself. Now, he claims that he too was a king in Jerusalem—re-enforcing his connection with the super-wise King Solomon.
He says that God has given humans an "unhappy business" to occupy their attention. It's just "chasing after wind"—a little like this Sixties folkie's ballad.
The Teacher says he, as King of Jerusalem, had more wisdom than anyone before him. This doesn't sound exactly humble. Yet, then he said that he tried out both wisdom and "madness and folly"—which means that he probably went to some pretty crazy parties. But this was just "chasing the wind" too.
He ends the chapter by saying that as you get more wisdom, you get more pain and sadness too. But, um, is that supposed to be wisdom, as well?