If you are using template column then you can bind your drop-down from mark-up using data-binding expressions. For example,
<asp:TemplateField HeaderText="XYZ">
<ItemTemplate>
<asp:DropDownList runat="server" ID="MyDD" DataSourceId="MyDataSource" />
</ItemTemplate>
</asp:TemplateField>
Above is assuming that your drop-down data in constant across rows. If it is changing then you can use data-binding expression such as
<asp:DropDownList runat="server" DataSource="<%# GetDropDownData(Container) %>" DataTextField="Text" DataValueField="Value" />
GetDropDownData will be a protected method in code-behind that will return the data (data-table, list, array) for the given row.
You can use GridView.RowDataBound event (or RowCreated event) in code-behind to fill drop-downs. For example,
protected void GridView_RowDataBound(Object sender, GridViewRowEventArgs e)
{
if(e.Row.RowType == DataControlRowType.DataRow)
{
// Find the drop-down (say in 3rd column)
var dd = e.Row.Cells[2].Controls[0] as DropDownList;
if (null != dd) {
// bind it
}
/*
// In case of template fields, use FindControl
dd = e.Row.Cells[2].FindControl("MyDD") as DropDownList;
*/
}
}