using System;
using System.Collections;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Diagnostics;
using System.Drawing;
using System.Drawing.Drawing2D;
using System.IO;
using System.Reflection;
using System.Runtime.InteropServices;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading;
using System.Windows.Forms;


class IeSample
{
    const int READYSTATE_COMPLETE = 4;

    static void GoogleSearchWithIE(string keyword)
    {
        Type comType = Type.GetTypeFromProgID("InternetExplorer.Application");
        dynamic ie = Activator.CreateInstance(comType);

        try {
            ie.Navigate("https://www.google.com/");

            while ( ie.Busy || ie.ReadyState < READYSTATE_COMPLETE ) {
                Thread.Sleep(50);
            }

            ie.Visible = true;

            dynamic html = ie.Document;

            dynamic t = html.getElementsByTagName("input");

            try {
                // Dump(t);

                if ( t["q"] == null ) {
                    Console.WriteLine("cannot find target element.");
                }
                else {
                    t["q"].Value = keyword;

                    dynamic form = html.forms("tsf");
                    if ( form == null ) {
                        Console.WriteLine("cannot find target form.");
                    }
                    else {
                        try {
                            form.submit();
                        }
                        finally {
                            Marshal.ReleaseComObject(form);
                        }
                    }
                }
            }
            finally {
                Marshal.ReleaseComObject(t);
            }
        }
        finally {
            Marshal.ReleaseComObject(ie);
        }
    }

    static void Dump(dynamic t)
    {
        for ( int i=0 ; i<t.Length ; i++ ) {
            Console.WriteLine("----");
            Console.WriteLine(t[i].Name??"");
            Console.WriteLine(t[i].Type??"");
            Console.WriteLine(t[i].Value??"");
        }
    }

    [STAThread]
    static void Main()
    {
        GoogleSearchWithIE("qiita");
    }
}

<form class="tsf nj" action="/search" style="overflow:visible" id="tsf" method="GET" name="f" onsubmit="return q.value!=''" role="search">...
<input class="gLFyf gsfi" maxlength="2048" name="q" type="text" ...>