How to implement a Stop/Cancel button?

Use a BackgroundWorker.

Put the heavy code in the DoWork event.

The cancel button should call CancelAsync on the BackgroundWorker.

In the heacy code in DoWork check the CancellationPending property periodically. If the property is true you should abort the work.

BackgroundWorker.CancelAsync Method is what you need. Here is a good example for you.

If you have got a time consuming process you will have to use a separate thread to handle that in order to support for cancellation. If you execute that time consuming process in the main thread(UI thread) it will be busy and won't take your cancellation request in to account until it finish that task. That's why you experience UI freezing.

If you use a backgroundWorker for your time consuming task and if you check the CancellationPending flag in the BackgroundWorker.DoWork method you could achieve what you want.

using System;  
using System.Collections.Generic;  
using System.ComponentModel;  
using System.Data;  
using System.Drawing;  
using System.Text;  
using System.Windows.Forms;  

namespace BackgroundWorker  
{  
    public partial class Form1 : Form  
    {  
        public Form1()  
        {  
            InitializeComponent();  

            //mandatory. Otherwise will throw an exception when calling ReportProgress method  
            backgroundWorker1.WorkerReportsProgress = true;   

            //mandatory. Otherwise we would get an InvalidOperationException when trying to cancel the operation  
            backgroundWorker1.WorkerSupportsCancellation = true;  
        }  

        //This method is executed in a separate thread created by the background worker.  
        //so don't try to access any UI controls here!! (unless you use a delegate to do it)  
        //this attribute will prevent the debugger to stop here if any exception is raised.  
        //[System.Diagnostics.DebuggerNonUserCodeAttribute()]  
        private void backgroundWorker1_DoWork(object sender, DoWorkEventArgs e)  
        {  
            //NOTE: we shouldn't use a try catch block here (unless you rethrow the exception)  
            //the backgroundworker will be able to detect any exception on this code.  
            //if any exception is produced, it will be available to you on   
            //the RunWorkerCompletedEventArgs object, method backgroundWorker1_RunWorkerCompleted  
            //try  
            //{  
                DateTime start = DateTime.Now;  
                e.Result = "";  
                for (int i = 0; i < 100; i++)  
                {  
                    System.Threading.Thread.Sleep(50); //do some intense task here.  
                    backgroundWorker1.ReportProgress(i, DateTime.Now); //notify progress to main thread. We also pass time information in UserState to cover this property in the example.  
                    //Error handling: uncomment this code if you want to test how an exception is handled by the background worker.  
                    //also uncomment the mentioned attribute above to it doesn't stop in the debugger.  
                    //if (i == 34)  
                    //    throw new Exception("something wrong here!!");  

                    //if cancellation is pending, cancel work.  
                    if (backgroundWorker1.CancellationPending)  
                    {  
                        e.Cancel = true;   
                        return;  
                    }  
                }  

                TimeSpan duration = DateTime.Now - start;  

                //we could return some useful information here, like calculation output, number of items affected, etc.. to the main thread.  
                e.Result = "Duration: " + duration.TotalMilliseconds.ToString() + " ms.";  
            //}  
            //catch(Exception ex){  
            //    MessageBox.Show("Don't use try catch here, let the backgroundworker handle it for you!");  
            //}  
        }  

        //This event is raised on the main thread.  
        //It is safe to access UI controls here.  
        private void backgroundWorker1_ProgressChanged(object sender,   
            ProgressChangedEventArgs e)  
        {  
            progressBar1.Value = e.ProgressPercentage; //update progress bar  

            DateTime time = Convert.ToDateTime(e.UserState); //get additional information about progress  

            //in this example, we log that optional additional info to textbox  
            txtOutput.AppendText(time.ToLongTimeString());  
            txtOutput.AppendText(Environment.NewLine);              
        }  

        //This is executed after the task is complete whatever the task has completed: a) sucessfully, b) with error c)has been cancelled  
        private void backgroundWorker1_RunWorkerCompleted(object sender,   
            RunWorkerCompletedEventArgs e)  
        {  
            if (e.Cancelled) {  
                MessageBox.Show("The task has been cancelled");  
            }  
            else if (e.Error != null)  
            {                  
                MessageBox.Show("Error. Details: " + (e.Error as Exception).ToString());  
            }  
            else {  
                MessageBox.Show("The task has been completed. Results: " + e.Result.ToString());  
            }  

        }  

        private void btoCancel_Click(object sender, EventArgs e)  
        {  
            //notify background worker we want to cancel the operation.  
            //this code doesn't actually cancel or kill the thread that is executing the job.  
            backgroundWorker1.CancelAsync();  
        }  

        private void btoStart_Click(object sender, EventArgs e)  
        {  
            backgroundWorker1.RunWorkerAsync();  
        }  
    }  
}  

stops the processing wherever it's at

If you mean that the process should stop immediately and not even wait for a moment where it checks a cancellation token, you may consider running the process in a separate AppDomain and kill it when you cancel.

Although this is perfectly possible, I would recommend a controlled termination as in the other answers, especially when your process changes external state.