Who will pay me for doing it anyway?

Web companys that handle advertising like that. They got paid from other companys, which they advertise. They are sending those links to members, members click them. Companys that paid for advertise make an evidence of how many times people get on there pages and they pay those web companys that in the end - pay you.

How does this "clicking" steals my time and bandwith?

It doesn't. The time you take to once a day check your mail and click some time around never last long. You see...when you join, they send you some mail every day. All you do is click on the hyperlink that leads you to certain page, on which you usualy have to stay from 30 to 90 seconds. Once time is up, you get transaction to your membership account.

Tell me all about paying.

After you reach a certain amount (usualy 10$, 50$, 200$ and more) you can demand money to be send on your internet-transaction account (PayPal, E-Gold, StormPay, MoneyBookers ...). From those internet-transaction providers you can easily send it to your credit card, check, etc. How much you get payed dependes on those advertising companys you join to.

Can you confirm this isn't just a waste of time? Have those transactions really happened?

Certainly. Below I pasted some links to pages, on which you can get the money 99%. Where is that 1% you guess? Well, companys could go off and stop working, but those linked below are running bussines succesfully and you don't have to fear. I personaly made some money, so I think anyone that is prepared to sacrifice few minutes a day and be patient, could make out nicely.

Let's say I join, at least to see how this stuff works. Do you have any tips for me?

Get a new e-mail account. Try something that has a lot of space and doesn't block spam. If you get tired of the whole thing you simply delete your account and no mail will be delivered to your adress anymore. Check account daily and click at connections that has word "runner" in it. Stay on those pages until you see that time is up. And just one thing - making money like this is not a mine gold if you don't just give up. At first you might be sceptic but as soon as you will get your first money from this thing in your hands, you will feel like - it was actualy the most easiest thing that brought you money ever.