The lawyer referred to in that article is suing in his capacity as the recipient of spam emails under California's anti-spam law.
Not every jurisdiction has a law like this. I'm from Australia. In Australia, when we make laws prohibiting something, the law usually appoints a government agency to administer the law and bring prosecutions under it, and fines are paid to the government. In contrast, America has a lot of these laws where affected individuals can sue and collect the fines personally.
So under the Californian law, you can get $1,000 per email for particular kinds of spam even if you haven't actually suffered any real damage: California Business and Professions Code s 17529.5(b)(1)(B)(ii).
How? You need to work out who sent the spam, get evidence to prove it, and file a claim in a Californian court. Apparently you can sue in small claims court, which saves you on filing fees.
It helps if you have many email accounts, because then you will receive many emails and therefore can collect many fines.
One of that lawyer's wins was in Balsam v Trancos (2012) in the Californian Court of Appeal.
Another example of a judgment discussing the Californian anti-spam law is Bontrager v Showmark Media.