Whether you are looking to adopt a pet from a shelter or breed-specific rescue organization, or buy a purebred show dog with papers and a pedigree, there is only one way to carry out the process: in person. You must be allowed to visit the shelter or breeder and meet the animals and bring them to your home yourself.
Anything else runs an extremely high probability of falling victim to a pet scam. Since the beginning of the coronavirus pandemic, concerns over in-person transactions have caused a drastic increase in this type of fraud. It is better to simply wait until after the pandemic to find your dog than to throw away hundreds (or thousands) of dollars.
The pet scam usually begins with either a website that appears to be a legitimate breeding business, or an advertisement on a website like Craigslist. They offer purebred animals with papers for very low prices, and always include plenty of adorable puppy photographs.
When you contact the breeder, they will come up with a reason you cannot visit the dogs in person (again, finding a ready-made excuse in the pandemic), and will offer to ship the animal to you. They will request payment for the dog, plus paperwork, air travel costs, and anything else they can come up with. They will also insist that payment be made with the usual non-traceable, non-retrievable methods: peer-to-peer payment apps (CashApp, Venmo, etc.), wire transfer via Western Union, cryptocurrency such as Bitcoin, or gift card numbers and access codes.
It is not difficult to guess what happens next: the victim never gets a dog, and their money is gone. In some cases, the scammers will set up a website for a fake shipping company, or even a lookalike airline website, and show their victims "tracking info" to "prove" their pet is on its way. Inevitably, some sort of problem occurs that requires the victim to send even more money. If the victim gets wise, the scammer may threaten to report them to the police for "animal abandonment," in a last-ditch effort to scare a few more dollars out of them.
There are some high-tech ways to examine an alleged dog breeder's website. You could enter the website address into a tool such as https://www.ip-tracker.org/lookup/whois-lookup.php and find out how long the URL has been registered (scam websites appear and disappear quickly; if it was registered within the past year, it's a good indicator that the website is not legitimate). Or you could perform a reverse image search on the site's photos to see if they have been stolen from someone else's website (or reused across multiple fake breeder websites).
But you really do not need to put in that much work. As soon as someone selling a dog comes up with an excuse for not meeting in person and wants to ship the animal to you, that is an instant dealbreaker because that dog definitely does not exist.