When you hand in your notice, your employer has a few options.
1) accept your resignation and let you leave on the date you’ve specified;
2) try to convince you to stay; or
3) refuse to accept your resignation and dismiss you.
But this doesn't matter much as you're hell-bent and intent on quitting.
So what's next?
Infographic showing timeline of "what's next": From the point where you throw letter and quit
The first steps is where the employee makes personal consideration whether to stay or leave the company. There could be multiple push pull factors, to attract an employee to greener pastures or to prevent him from leaving a familiar environment. Change isn't comfortable here.
The second step is about the employee's formal decision to quit. Day 1 of notice starts here (same day).
Then, handover of duties start. Work goes on as per normal, the resigning worker still comes to office as per usual, with gradually fewer duties.
Finally, as the last day of notice and workday ends, the obligation to remain at the company terminates. Then he is free to engage in fresh work, employment or reclaim his free time to do whatever else he has planned.
This process consists of many steps, but it is not a lengthy process. Many people have quit and gone through this before. Plus the company will already have their own backup plans in place to maintain their business structure and continue current projects.