Sharing data between threads of different methods

The usual method is to use locks (as you would if it were the same method) to achieve predictable behavior though you might need to use other techniques as well.

For example, if we make your code into an executable program and run it multiple times:

using System;
using System.Threading;

class Program
{
    string shareme;
    static Program p = new Program();

    static void Main()
    {
       Program p = new Program();
       Thread t1 = new Thread(p.A);
       Thread t2 = new Thread(p.B);
       t1.Start();
       t2.Start();
       p.shareme = "Updated in main";
       Console.WriteLine(p.shareme);
       Console.ReadKey();
    }

    void A()
    {
       p.shareme = "Updated in A";
       Console.WriteLine(p.shareme);
    }

    void B()
    {
       p.shareme = "Updated in B";
       Console.WriteLine(p.shareme);
    }

}

The order of the output is completely unpredictable. It might be :

Updated in main
Updated in A
Updated in B

bit it could be other permutations as well.

Suppose we wanted it to always be:

Updated in A
Updated in B
Updated in main

then we could achieve that by adding a lock in A() and then 'joining' both threads in the main thread so that the latter's Console.WriteLine always executes last:

using System;
using System.Threading;

class Program
{
    static object padLock = new object();

    string shareme;
    static Program p = new Program();

    static void Main()
    {
       Program p = new Program();
       Thread t1 = new Thread(p.A);
       Thread t2 = new Thread(p.B);
       t1.Start();
       t1.Join();
       t2.Start();
       t2.Join();
       p.shareme = "Updated in main";
       Console.WriteLine(p.shareme);
       Console.ReadKey(); 
    }

    void A()
    {
       lock(padLock)
       {
         p.shareme = "Updated in A";
         Console.WriteLine(p.shareme);
       }
    }

    void B()
    {  
       p.shareme = "Updated in B";
       Console.WriteLine(p.shareme);
    }
}

The lock ensures that the B thread doesn't have a chance to update shareme before thread A can print it to the console.