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

namespace WindowsFormsApplication1
{
    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();
        }

        Form2 form2;
        private void Form1_Load(object sender, EventArgs e)
        {
            form2 = new Form2();
            form2.Show();
        }

        private void button2_Click(object sender, EventArgs e)
        {
            form2.hoge = textBox1.Text;
        }

        private void button1_Click(object sender, EventArgs e)
        {
            form2.TextClear();
        }
    }
}

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

namespace WindowsFormsApplication1
{
    public partial class Form2 : Form
    {
        public Form2()
        {
            InitializeComponent();
        }
        public string hoge
        {
            set { textBox1.AppendText(value); }
        }
        public void TextClear()
        {
            textBox1.Clear();
        }
    }
}