The statement you have entered would allow for spaces in front of the first name and after the first name before the wildcard search. If you want to search for any part of a first name, you should change your SQL to something like this:
SELECT empID FROM emp WHERE FirstName LIKE '@FirstName%'
Also, it's much safer to use parameretized queries like this versus just concatenating your arguments:
StringBuilder sb = new StringBuilder();
sb.Append("SELECT empID FROM emp WHERE FirstName LIKE '@FirstName%'");
SqlConnection conn = new SqlConnection(connStr);
SqlCommand command = new SqlCommand(sb.ToString());
command.CommandType = CommandType.Text;
command.Parameters.AddWithValue("FirstName", textbox1.Text);
DataTable dt = new DataTable();
SqlDataAdapter da = new SqlDataAdapter(command);
da.Fill(dt);
If you want to use a stored procedure, you'll need to setup your SqlCommand object like so:
SqlCommand command = new SqlCommand("Procedure", conn);
command.CommandType = Command.StoredProcedure;