You know a guy who knows a guy
“You’re going to join the rebellion?” he started. “You’ve got to be kidding. How?”
“Damp down, will you?” the bigger man cautioned, glancing furtively back toward the power station. “You’ve got a mouth like a crater.”
“I’m sorry,” Luke whispered rapidly. “I’m quiet—listen how quiet I am. You can barely hear me—”
Biggs cut him off and continued. “A friend of mine from the Academy has a friend on Bestine who might enable us to make contact with an armed rebel unit.”
“A friend of a—You’re crazy,” Luke announced with conviction, certain his friend had gone mad. “You could wander around forever trying to find a real rebel outpost. Most of them are only myths. This twice removed friend could be an Imperial agent. You’d end up on Kessel, or worse. If rebel outposts were so easy to find, the Empire would have wiped them out years ago.”
“I know it’s a long shot,” Biggs admitted reluctantly. “If I don’t contact them, then”—a peculiar light came into Biggs’s eyes, a conglomeration of newfound maturity and … something else—“I’ll do what I can, on my own.” - Star Wars: A New Hope - Official Novelisation
You form a cell, then do some low-level stuff against the Empire
In Star Wars: Rebels, our rebellious heroes are actually unaware that they're working for the Rebellion proper. Only Hera has a connection to a planner, unaware that that planner; Fulcrum is actually a part of the Rebellion against the Empire.
When the time was right and they'd proven themselves to be both reliable and ideologically sound, the crew were invited to become part of the main cell. They were then tasked with recruiting others to join the fight, resulting in the formation of other small Rebel cells.
You keep your ear to the ground and hope someone makes contact with you
“Hey,” he said. “Can’t sleep?”
Lohgarra admitted she’d woken up hungry, then said Thane looked worried.
“‘Worried’ isn’t exactly the word.” The number of people he trusted enough to share this with could have been counted on one hand, with fingers left over—but Lohgarra was among them. “Lieutenant Commander Antilles, from the, uh, unaffiliated group earlier today? He wants me to fly with them.”
That earned a roar of indignation. How dare that man try to steal her best pilot? Taking advantage of a crisis like that was unthinkable. She’d see to it that Thane got a raise, if that was what it took to keep him—
“No, no, Lohgarra, you don’t understand.” Thane lowered his voice. “They’re with the Rebellion.” - Journey to Star Wars: The Force Awakens - Lost Stars
Some Rebel units host open recruitment sessions on planets that they've (temporarily) liberated from Imperial control
When the civilians came out of hiding and into the plaza, the open recruit began.
Sergeant Zab’s squad—the squad Namir had once called, in a moment of pique, “morons who could make a hydrospanner backfire”—had somehow smuggled an astromech droid into the city surveillance center. From there, they’d accessed the public address system and broadcast the captain’s message: Twilight Company would soon depart Haidoral Prime. Those on Haidoral who shared the Rebellion’s ideals of freedom and democracy could remain to defend their homes, or they could sign on with Twilight to take the fight to the enemy. To go where the Rebellion was needed most. And so forth.
The captain recorded a new broadcast every time Twilight went looking to bolster its ranks, tailored to the needs and the circumstances of the local population. To Namir, all the messages sounded alike.
Open recruitments were technically against Rebel Alliance security policy, but they were a Twilight Company tradition and the captain was insistent the practice continue. So long as the Rebellion sent Twilight into hell time and again—and so long as Twilight survived—the company would replenish its losses from the ranks of the willing - Star Wars: Battlefront - Twilight Company