First pick a country with a working rule of law. The US or UK are good choices, people there respect the law.
Now, make somebody up. This person needn't really exist, but they should be plausible enough for the foreign court to believe by default that they do, call them, say, Sergei Petrov. See, that's a Russian name, so why not. Sergei Petrov from, say, Moscow.
Now, hire expensive lawyers in the target country to sue the individual whose life you want to ruin. Tell them that lucky Sergei Petrov has a patron, who must remain anonymous but has given him money to sue the defendant because of how outrageous whatever it is they did was. Alas Sergei communicates only through typed letters and muffled telephone calls.
The lawyers will inform their court that Sergei can't travel, but they'll present his case anyway. The court will agree to hear the case.
The defendant spends lots of money on their lawyers. They win easily since Sergei's case is complete bunk.
The court says "Hey, this was frivolous crap, Sergei owes the defendant money!". Alas your lawyers will inform the court that Sergei has mysteriously vanished, as has the money of his anonymous sponsor. Oh dear.
Now, to be fair this costs the Russians lots of money - fancy foreign lawyers are expensive, and of course they tacitly know this is a scam so they'll charge plenty to help facilitate it. But the defendant is left out of pocket and stressed. So it's effective for annoying people.
I would hope that knowingly being a part of something like this is the type of thing that gets one disbarred.