I am a little confused but I am learning, here is the code I have behind the listing of students with the button. The form that will house the student details is called studentdetails. All of this is a web form like you suggested.

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

namespace Project
{
    public partial class StudentListdb : Form
    {
        public StudentListdb()
        {
            InitializeComponent();
        }
        DataTable dt;

        private void TextBox1_TextChanged(object sender, EventArgs e)
        {
            DataView dv = new DataView(dt);
            dv.RowFilter = string.Format("name LIKE '%{0}%'", textBox1.Text);
            dataGridView1.DataSource = dv;

        }

        private void Showstudentsdb_Load(object sender, EventArgs e)
        {
            SqlConnection con = new SqlConnection(@"Data Source=server;Initial Catalog=db;Integrated Security=True");
            con.Open();
            SqlCommand cmd = new SqlCommand("SELECT E.SCH_YR AS School_Year, E.STU_ID AS StudentID, ISNULL(E.NAME_F_LNG, '') + ' ' + ISNULL(E.NAME_M_LNG, '') + ' ' + ISNULL(E.NAME_L_LNG, '') AS Name, E.GRD_LVL AS [Grade Level], E.CAMPUS_ID AS SchoolBuildingCode, CL.CAMPUS_NAME, D.unique_stu_id AS StateStudentID, case when E.ACTIVE_CD = 1 then 'Active' Else '' end AS status, D.SEX AS gender, REPLACE(D.email, '@g.aledoisd.org', '@aledoisd.org') AS email FROM[rsccc].[SR_STU_ENROLL] AS E INNER JOIN [rsccc].[SR_STU_DEMO] AS D ON E.STU_ID = D.STU_ID AND D.SCH_YR = E.SCH_YR LEFT OUTER JOIN [rsccc].[CR_DEMO] AS CL ON E.SCH_YR = CL.SCH_YR AND E.CAMPUS_ID = CL.CAMPUS_ID WHERE(E.SCH_YR =(SELECT MAX(SCH_YR) AS Expr1     FROM[rsccc].[DR_CURRICULUM_CYR] AS DR_CURRICULUM_CYR_1)) AND(E.STATUS_CD <> 4) AND(E.STATUS_CD <> 5) AND(E.ACTIVE_CD = 1) ORDER BY SchoolBuildingCode, StudentID, [Grade Level] ", con);
            SqlDataAdapter da = new SqlDataAdapter(cmd);
            dt = new DataTable();
            da.Fill(dt);
            dataGridView1.DataSource = dt;
            DataGridViewButtonColumn btn = new DataGridViewButtonColumn();
            dataGridView1.Columns.Add(btn);
            btn.HeaderText = "Student Details";
            btn.Text = "Student Details";
            btn.Name = "btn";
            btn.UseColumnTextForButtonValue = true;

         
            dataGridView1.BorderStyle = BorderStyle.None;
            dataGridView1.AlternatingRowsDefaultCellStyle.BackColor = Color.FromArgb(238, 239, 249);
            dataGridView1.CellBorderStyle = DataGridViewCellBorderStyle.SingleHorizontal;
            dataGridView1.DefaultCellStyle.SelectionBackColor = Color.SeaGreen;
            dataGridView1.DefaultCellStyle.SelectionForeColor = Color.WhiteSmoke;
            dataGridView1.BackgroundColor = Color.FromArgb(30, 30, 30);
            dataGridView1.RowHeadersWidthSizeMode = DataGridViewRowHeadersWidthSizeMode.DisableResizing;//optional
            dataGridView1.EnableHeadersVisualStyles = false;
            dataGridView1.ColumnHeadersBorderStyle = DataGridViewHeaderBorderStyle.None;
            dataGridView1.ColumnHeadersDefaultCellStyle.Font = new Font("MS Reference Sans Serif", 10);
            dataGridView1.ColumnHeadersDefaultCellStyle.BackColor = Color.FromArgb(37, 37, 38);
            dataGridView1.ColumnHeadersDefaultCellStyle.ForeColor = Color.White;
            for (int i = 0; i < dataGridView1.Columns.Count; i++)
            {
                dataGridView1.Columns[i].AutoSizeMode = DataGridViewAutoSizeColumnMode.AllCells;
                int colw = dataGridView1.Columns[i].Width;
                dataGridView1.Columns[i].AutoSizeMode = DataGridViewAutoSizeColumnMode.None;
                dataGridView1.Columns[i].Width = colw;
            }



            
        }
       
        private const int StudentDetailsColumnIndex = 0;

        private void TextBox2_TextChanged(object sender, EventArgs e)
        {
            DataView dv = new DataView(dt);
            dv.RowFilter = string.Format("StudentID LIKE '%{0}%'", textBox2.Text);
            dataGridView1.DataSource = dv;
        }
     
    


        private void Button1_Click(object sender, EventArgs e)
        {
            Application.Exit();
        }
    }
}