Once references are added, import the namespace we will be using as below:
using Smartsheet.Api;
using Smartsheet.Api.OAuth;
using Smartsheet.Api.Models;

Now we can use Smartsheet object to connect and insert data into smartsheet. All you need is Smartsheet ID and Smartsheet API Token. Below is the code:

string smartsheetAPIToken = “xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx”;
long sheetID = xxxxxxxxxxxxxxxxx; //Smartsheet ID
Token token = new Token();
token.AccessToken = smartsheetAPIToken;
SmartsheetClient smartsheet = new SmartsheetBuilder().SetAccessToken(token.AccessToken).Build();
Sheet sheet = smartsheet.SheetResources.GetSheet(sheetID, null, null, null, null,null, null, null);

//Code to read data table exported from SQL:

OleDbDataAdapter da = new OleDbDataAdapter();
DataSet ds = new DataSet();
DataTable dt = new DataTable();

//Loop through the data table.

foreach (DataRow dRow in dt.Rows)
{

//Code to read column name in Smartsheet i.e. Top Row

Row nRow = new Row();
foreach (Row topRow in sheet.Rows)
{
nRow = topRow;
}

//Define Cell and create object mapped with each column

Cell ID = getCellByColumnName(nRow, “ID);
Cell Name = getCellByColumnName(nRow, “Name”);
Cell Address = getCellByColumnName(nRow, “Address”);
Cell Email = getCellByColumnName(nRow, “Email”);

//Assign data to be inserted to each Cell

ID.Value = Convert.ToString(dRow[“ID”]);
Name.Value = Convert.ToString(dRow[“Name”]);
Address.Value = Convert.ToString(dRow[“Address”]);
Email.Value = Convert.ToString(dRow[“Email”]);

var cellsToAdd = new List();
cellsToAdd.Add(ID);
cellsToAdd.Add(Name);
cellsToAdd.Add(Address);
cellsToAdd.Add(Name);

//Add row to smartsheet

row = new Row.AddRowBuilder(true, null, null, null,
null).SetCells(cellsToAdd).Build();

smartsheet.SheetResources.RowResources.AddRows(sheetID, new Row[] { row });
}

Below is the function getCellByColumnName used in the above code.
public Cell getCellByColumnName(Row row, string columnName)
{
return row.Cells.First(cell => cell.ColumnId == columnMap[columnName]);
}
Once your done with the code. Please save and close the code window and click OK to script task. Now your SSIS package will look like below: