How hard is it?
Very hard.
Despite this, certain individuals and groups have been peculiarly lucky in this regard. Catchphrases come to mind as a good example. The programs Laugh-In and Saturday Night Live succeeded in introducing slang phrases which became peculiarly popular for a time. Then again, they probably tried to introduce a bunch which flopped.
Certain films were written with a deliberate intention to develop a popular catchphrase which would serve to promote the film. Each of the Dirty Harry films has a phrase Clint Eastwood uses ad nauseum. Some of them caught on, such as “make my day”. Others, such as “mar-vel-lous”, did not.
After Max Factor Jr. died, Aliester Cooke observed on his Letter from America broadcast that Factor had introduced at least two expressions still in widespread use. One of them was “pancake” to mean a particular type of makeup; I don’t recall what the other was. Cooke observed that it was very unusual for a prominent person to add even one expression to current use, and told about how he had once tried to do that himself. (He thought up a nickname for sandwiches with grilled American cheese, naming them after a crooked businessman who was in the news at the time, being "grilled’ by a Congressional committee. The expression got a local currency, then died out in a few weeks.)
Some years ago David Letterman undertook an experiment to introduce a new catchphrase. He tried twice. The first was “I do and I do and I do for you kids, and this is the thanks I get?” The second was “They pelted us with rocks and garbage”. Despite extensive effort,neither, obviously, caught on.
Spy Magazine used to run an ongoing feature about an aspiring cartoonist who was hoping that his (or her) creation, the “muffin people”, would catch on in the manner of troll dolls or The Smurfs. They didn’t.