You'd likely have to save up money to leave, which might be hard as a sharecropper as your "employer" controls all the books and can effectively fine-tune your net income to be near zilch. You might also be in debt, which could be enormously difficult to get out from under legally. And, your "employer" might not want you to go, so you may have to make plans entirely in secret and leave carefully and suddenly. Indeed, if they found out you were leaving they may take drastic action, including lynching to "provide a lesson".

Meanwhile, how are you traveling? You can't just walk from South Carolina to New York in any practical sense in the 1930s, certainly not as a person of color. That leaves buses, trains, and an automobile. It's unlikely that as a sharecropper you would own an automobile, though if you had you might find it a bit of a hassle to get to NYC. Many hospitality establishments (restaurants, hotels, etc.) along the way would refuse you service. If you could make the trip all in one day that would be ideal, having to find a place to sleep would be a nightmare, and unlikely to be successful. By the later 1930s the Green Books started to be printed and if you traveled then you might have the benefit of being able to find waypoints for food and lodging along the way that were safe, and the journey might be a bit easier. Still traveling the open roads as a black man in 1930s America would be a recipe for the sort of spontaneous "adventures" that nobody desires, you might get lucky and it might be uneventful, who knows.

If you were traveling by train you would have been segregated into the Jim Crow car, with decidedly inferior accommodations compared to what the white passengers could enjoy (though the fare was identical). You would have to plan ahead and bring your own food (a common tactic was to pack meals using somewhat travel friendly foods like fried chicken and hard boiled eggs into a shoe box) and then you'd just have to suffer through the extremely long trip crammed into the car amongst the luggage of the rest of the train. It would take the better part of a day to reach New York from South Carolina by train in the 1930s, and your only accommodation would be a tiny hardback seat.

The other side of the equation is, why Harlem? What do you plan to do once you're there? And where do you plan on staying? In the 1930s it would have been difficult to find decent employment anywhere, and NYC was no exception. You would almost certainly not choose to venture up to Harlem (or off to any of the other Great Migration destination spots like Los Angeles, Oakland, Chicago, etc.) without some connection there already. A relative or a friend or at least someone you had a connection to. Some place you can stay until you get on your feet, someone who can give you the lay of the land and get you pointed in the right direction in terms of finding a job. Some folks certainly traveled "blind" during the Great Migration, but it was the extreme exception.

Anyway, to focus more on the specifics of conditions in South Carolina, things would have been bad. Things were bad everywhere in America, to be honest, but in the South they were enough to cause one of the most significant refugee crises in modern history. It's easy to imagine the Jim Crow South as a monolithic and unchanging chunk that occupies a certain volume of space and time from after reconstruction up through the civil rights movement until it goes away, but the reality was that it was dynamic, constantly changing, evolving, mutating, acting, and reacting all throughout this period. Most relevantly, it was entrenching itself deeper and deeper into a very strong caste system with black Americans as a permanent, powerless underclass. Bit by bit, day by day. It was doing this through legal means, through cultural shifts, and through systematic and spontaneous acts of terrorism which included lynchings but also included beatings and other forms of violence as well as more subtle means of putting the under-caste in its place.

You can explore a map of reported lynchings in America, here: https://lynchinginamerica.eji.org/explore

As you can see, South Carolina certainly had its fair share.

I'll include a short excerpt here from Isabel Wilkerson's The Warmth of Other Suns:

Van Vleet, Mississippi, 1928

Ida Mae Brandon Gladney

[...]

In the bottoms where Ida Mae grew up, it was a crazy enough world that they could almost time the weekends by a white farmer who lived down the road.

He was fine when he was sober and actually liked colored people. But he got drunk on Fridays and came staggering on his old horse to the colored people's cabins. They could hear the hoof steps and hollering as he rode in waving his gun.

"I'm coming through!" he shouted.

Grown people dropped their buckets and went running. Children hid under the cabins on the dirt floor between the stilts, while he huffed and cussed and tried to smoke them out.

"I'm a shoot y'all!" he hollered. "I'm a kill y'all!"

There was always a commotion and a panic whenever he came through. It could happen day or night. There was never much warning, and they had to scramble to escape his ragged gunshots. Then they had to lie perfectly still. "We'd run under the house, and, wherever he hear a bump, he would shoot," Ida Mae said.

One day when he came through, Ida Mae was outside and couldn't get under the house in time. Josie and Talma had scattered already, and she didn't see where they had gone. The man had wobbled off his horse and was coming through, firing his gun.

A barrel of cornmeal was right next to her, and she saw it and jumped inside. She sank into the grit cushion of meal with her chin digging into her knees. All the while, the man hollered and grunted around her, and the bullets made the pinging noises of metal against tin. She pulled the top over her head and tried not to breathe. She stayed in the barrel until the shooting and the cussing stopped.

He was drunk and a bad aim and never actually hit anybody as far as Ida Mae knew. No sheriff or police were ever called in. There would have been no point in calling. And so the drunk farmer could go on shooting and scaring the Brandons and other colored people in the bottoms whenever he felt like it.

As she grew older, she learned that there was more to the southern caste system than verbal slights and the antics of a crazy white farmer. In the summer of 1926, when she was thirteen, a cloud passed over the grown people, and it showed in their faces. She could overhear them whispering about something that had happened in town, some terrible thing they didn't want the children to know about. It had to do with two colored boys - the Carter brothers, as she heard it - and a white woman.

"They said something to the white lady," she said.

And, as best as Ida Mae could make out, the white people had taken the boys and hanged them in Okolona that morning. [...]

Every person of color living in the South would have had a story of some variety that would be of a similar character, even in South Carolina. In the South blacks had no rights, and their lives were but playthings for the white population.This was made clear hour after hour, day after day, decade after decade with language, with treatment on the streets, with violence, and with lynchings. This was true everywhere in America, but outside of the South it was significantly less severe.

I highly recommend reading The Warmth of Other Suns it tells the story of the great migration primarily through three different accounts from very different backgrounds (including a sharecropper!) and different time periods. It gives a sense of the conditions they left, the difficulties of the journeys, and the difficulties of making new lives where they ended up.