As a regular Internet user, I am frequently asked to sign, and spread, on-line petitions. I must admit I do sign some, but hold very little faith in their effectiveness. In contrast there are other, more effective ways of eliciting change.
On-line petitions are not taken seriously, since they are easy to falsify and it is hard to verify the legitimacy of the signers. They may not even be from the country or area in reference to the petition itself. It could be one person, with multiple e-mail addresses, signing a repeated number of times. Sometimes petitions are circulated via e-mail and people sign without reading the issue. Since they are fairly anonymous, the on-line petitions are often disregarded. To be fair, petitions in general are easy to falsify, assuming nobody checks each signature. Another problem is that sometimes you get so many petitions for the same cause. As such petitions on the whole are somewhat weak.
Action is a far better tactic than an on-line petition. Action is direct and puts your credibility of belief on the line. Nobody can question your loyalty to the cause if you put your face forward and act. Many people do not act, because they do not know what to do, or they have the excuse that they do not have the time. In fact if you believe in something strong enough, you will find the time to effect a change, and no, you do not need to be wealthy to do so, you merely need to be passionate.
I caution you that the result will depend heavily on whom or what you are up against, how many people are willing to act without, and your methods as a whole. You will note that some causes have better chances than others, of being rectified.
Some popular causes are a call to end the ban wearing fur, a plea to stop puppy mills, or a call to bring back a favorite television show. All have had, or still have, on-line petitions. I suggest a more active approach.
If you are against people wearing fur, adding your signature is not going to stop people wearing fur. Dumping red paint on fur wearing people is illegal, although it has been done many times to shame those who wear fur. This has still not been effective. People will not stop wearing fur until it becomes unfashionable to do so. This is a trend that has started. Also you need to realize protesting people wearing leather is counter productive, leather is a by-product of the beef industry, it is better for people to wear leather than fur if you are trying to save animals from being killed for fur alone. Set an example by not wearing fur and not hanging around with people who do. This is going to be very hard to do, because not only do many people make money from the fur industry, but also many people enjoy the feeling of wearing fur.
If you want to stop puppy mills (places that supply pups to pet stores), you need to stop supporting any pet store that sells pups. Do not buy your pet food or any supplies there. Instead shop at a store that does not sell pups, for example at a groomer or livestock supply store, yes, they typically sell pet food too. Spread the word to others as to why they should not buy puppies from pet stores. This is going to be difficult because stores, and puppy mills, make their money breeding and selling puppies, nobody wants to lose income and they will deny to the public that the pups are from mills.
If you want a television network to renew a show, you can do it. In fact it has been done. As you have noticed, the other two cause examples were ones where people, or businesses, would suffer a financial loss of they were to change, or stop, doing what they are doing. With television networks and programming, all you have to do, is convince them they will make more money by renewing a show. In the United States, in 2007 a CBS drama, called Jericho, was canceled. Fans were outraged and, thanks to the wonders of the Internet, they met on line in forums and came together with a plan, or actually several plans, one of which was an on-line petition. How effective the petition was, cannot be known, but what probably had the most impact was the actions of many of these dedicated fans. They wrote to the network, called them, and eventually mailed them pounds and pounds of nuts. The nuts were a response to a comment made by one of the characters in the show. They even got the attention of other media, such as newspapers and magazines. Eventually CBS announced that the show would continue, the actions taken had resulted in a huge success.
So you see, it is what you DO that actually matters the most, and whom you do it to. If your cause is fighting an industry which makes money doing what it is doing, you need to get a whole lot of people together to educate others against supporting that industry, it is a slower battle than the relatively overnight success when you fight to get a result that has a win-win at the end of it.
I caution you not to do stupid or illegal things, as these will merely make you look foolish or discredit your cause. I suggest spreading awareness of the issue through writing letters to your local newspaper, or even on the Internet. Talk to people. Do things. Good Luck.