If you look at the data access part of asp.net/learn there's a ton of tutorials specifically surrounding data access through asp.net, although from what you've posted I suspect that this is "over-complicated" for what you're after.
At its simplest what you want to do is have your aspx page, lets call it default.aspx and have the following in it:
<asp:TextBox runat="server" ID="myTextBox">
</asp:TextBox>
<asp:Button runat="server" ID="myButton" OnClick="myButton_OnClick" Text="Click to save" />
Now in your codebehind file (the .aspx.cs file) you'll want to have an event handler for the Click event of myButton
protected void myButton_Click(object sender, EventArgs e)
{
var myConnectionString = "Connection String goes here";
using (SqlConnection conn = new SqlConnection(myConnectionString))
{
using (SqlCommand cmd = new SqlCommand("INSERT INTO dbo.mytable (fieldName) VALUES (@value1)", conn))
{
cmd.Parameters.Add(new SqlParameter("@value1", myTextBox.Text));
cmd.ExecuteNonQuery();
}
}
}
The example code above, for doing the database work, is very rudimentary and I strongly suggest you read some of the tutorials on asp.net/learn and elsewhere on the net (perhaps even the msdn documentation for SqlCommand, SqlParameter and SqlConnection) to familiarise yourself with what they are and how they work.