As publisher (website owner with ads on it), yes I make a small amount of money everytime a user clicks on it.
As an advertiser I'm charged by impressions (amount of times ad is shown).
There are other models in place, but this is the most common.
I wouldn't recommend clicking on lots of ads randomly, too many from the same IP / address / computer and it will be detected as click fraud and the advertiser will be reimbursed for it.
If you find the ad relevant click on it, if not don't .
They are more there as a supplemental income, to help cover costs. I dont' like intrusive ads on websites so I try to avoid placing them all over the shop.
As a publisher I can't click on them myself, its against the t&c's.
I considered placing them above or below the forum pages, but I didn't want to annoy the users of this site. Not sure how much income potential it would boost. Might pay for hosting all together, would have to test it out for a couple of months though.