From the Humane Society of the United States:

People tether their dogs for a variety of reasons. Most people who do this are unaware of the harm it can cause to their dogs. Social norms of pet-keeping have made tethering unpopular, so it is declining as a practice, but some reasons people do it include:

• The dog is a repeat escapee and the owner has run out of ideas to safely confine the dog.
  
• The owner is trying to protect their dog from something on the other side of their fence (kids, another dog, etc.) by keeping the dog in one area in the yard.
  
• The owner's fence is damaged or the owner doesn't have a fenced yard.
  
• The dog's behavior makes keeping them indoors challenging and the owner doesn't know how to correct the behavior.
  
• The landlord may not allow the pet owner to keep the dog indoors or install a fence.
  
• The pet owner comes from a family that always tethered dogs and may not realize there are better options.

If you're worried about a chained dog near you, there are many online guides — from Unchain Your Dog, Dogs Deserve Better, HSUS, Stray Animal Foundation, and others — that offer advice about how help. They suggest the following:

• Try speaking and offering help to the owner, trying to encourage bringing the dog inside. Learn why the owner won't bring the dog inside. (Dogs Deserve Better)
• If bringing the dog inside is not an option, offer help in the form of straw, food, and a dog house if needed. A warm shelter is better than no shelter at all. (Dogs Deserve Better)
• Offer to rehome or buy the chained dog from the owner. (But don’t offer to buy the dog if you think that the owner will just go right back out and get another.) Just say something like, “I saw your dog and have always wanted a red chow. Would you sell him to me for $50?” You can then place the dog into a good home. (Stray Animal Foundation)
• Consider asking your local animal care and control agency to pay the owner a visit. Even if tethering is legal, agents can make a friendly visit to see if they can improve the situation by helping the owner troubleshoot and gather resources to address the problem at its root. Most situations can be improved through positive engagement and support services; punitive measures can be used to address the most egregious of situations. (HSUS)

In some communities, there are also nonprofit organizations that provide care and outreach specifically for chained/outside dogs. An online search can help you find out whether there are any in your local area. If so, you can contact them for guidance or support.

UnchainYourDog.org offers tips on approaching dog "owners," including the following:

It is very important to be nice, friendly, and respectful to the dog’s owners.  

Say something like:

• I saw your dog in the backyard. I have a big bag of dog food I don't need any more. Could you use it? I'd hate for it to go to waste.
• I have an extra doghouse I'd be happy to bring over. Is that OK?
• I noticed your dog lives on a chain. I'm sure he would love the chance to exercise. Could I come by a few times a week to walk your dog?
• I love shepherds. My shepherd died and I really miss him. Can I go back and meet your dog? What's his name?
• Since winter is coming, I'm giving hay to people with outside dogs. Could you use some hay for your dog's house?

If the owner seems receptive, ask if you can go with the owner to meet the dog. Ask the dog’s name. This will give you an opportunity to get to know the dog and the owner, and to learn why the dog is on a chain. Sometimes you can help solve the problem.

It may take multiple visits to gain the owner's trust. Keep at it, and take baby steps each time you visit.

1. Educate the owner so that he will think of the dog in a new light; as a living creature who needs love and attention and care. Hopefully, he will learn how to treat dogs better in the future.
2. Helping the dog a little is better than doing nothing at all. You may not be able to convince the owner to relinquish the dog or put up a fence. If all you can do is get a decent doghouse, a well-fitting collar, and some treats, that is a success and the dog’s life has been improved.

Yes, some states and communities in the U.S. have laws regarding chaining and tethering. To see what laws may be on the books in your area, we recommend checking out PETA's list of Current Legislation on Tethering Dogs.

Additionally, Michigan State University explains how some of these laws work:

While the laws themselves vary from state to state, they do have several consistent features. Some state laws allow a dog to be tethered for a reasonable period of time. California prohibits tethering a dog to a stationary object, but allows a dog to be tethered “no longer than is necessary for the person to complete a temporary task that requires the dog to be restrained for a reasonable period.” More recent laws restrict the number of hours a dog can be tethered within a 24-hour period.

Some states specify the type of tether. Hawaii and Rhode Island and several others have outlawed choke collar, pinch collar, or prong type collars. Other states dictate the length or weight of the tether. Many states require that the tether allow the dog unencumbered access to food, water, and shelter without becoming entangled.

"Cruel" tethering may be included as a violation of state anti-cruelty chapters. Indiana defines “neglect” as restraining an animal for more than a brief period in a manner that endangers the animal's life or health by the use of a rope, chain, or tether. Tethering in a manner that causes injury or even danger to the dog, including attacks by other animals, can be classified as cruel restraint under many state laws.

Finally, in the wake of dogs being left tied during natural disasters, some states provide restrictions based on weather. Pennsylvania makes it a presumption of neglect if the dog is tethered for longer than 30 minutes in temperatures above 90 or below 32 degrees Fahrenheit. In Connecticut and Massachusetts, when a weather advisory or warning is issued by authorities, or when outdoor conditions (extreme heat, cold, wind, rain, snow or hail) pose an adverse risk to the health or safety of particular dog, duration of tethering cannot exceed fifteen minutes. In Louisiana, it is prohibited to tie or tether a dog or cat in a manner that exposes it to extreme weather conditions in designated emergency areas.

What happens in those states without laws? General anti-cruelty laws could still penalize the tethering if the dog suffers neglect or cruelty under state law. In addition, many cities and counties have implemented their own laws that restrict or regulate tethering and chaining. 

Absolutely! We recommend checking out PETA's guide to passing animal-friendly legislation.

Here is a good explanation from UnchainYourDog.org:

Chaining makes dogs aggressive — not protective. A dog learns to be protective by spending time with people and by learning to love his human family. When your dog loves you, he will want to protect you.

Aggressive dogs don’t know the difference between friends and enemies, because they are not used to people.

Plus: A chained dog can’t do anything to stop an intruder! All he can do is bark. If all you want is a burglar alarm, consider an electronic one.