There's a few steps to go through here - none of them are particularly difficult, but they can be a bit fiddly (IMHO). The good news is once you've got this working once, it gets easier to do it again!
I'm assuming you've got a <asp:*DataSource>
control on your page - my preference is for an ObjectDataSource but I don't think it matters, I think a SqlDataSource works equally well. I've never tried doing this with GridView.DataSource = MyDataSet
in code-behind, so I don't know whether that would work or not, but my assumption is that it wouldn't as you wouldn't get the proper two-way binding that you want. This data source feeds your grid with your main data. The key point here is that your database query must return both the Status text field and the Status id.
So your gridview will now look something like:
<asp:objectdatasource runat="server" id="MainDataSource" ... />
<asp:gridview runat="server" id="MyGridView" DataSourceID="MainDataSource">
<Columns>
<asp:TemplateField HeaderText="During Production Status" SortExpression="DuringProductionStatus">
<ItemTemplate>
<asp:Label ID="lblStatus" runat="server"
Text="<%# Bind('Status') %>" />
</ItemTemplate>
</asp:TemplateField>
</Columns>
</asp:gridview>
The Text="<%# Bind('Status') %>"
is the bit you're missing to get the status text into the grid.
Now add a second data source into your markup that reads in the set of values from the Status table.
<asp:objectdatasource runat="server" id="StatusObjectDataSource" ... />
And add the EditItemTemplate into the GridView, which is bound to the Status DataSource.
<EditItemTemplate>
<asp:DropDownList ID="ddlStatus" runat="server" datavaluefield="StatusID"
datatextfield="Status" DataSourceID="StatusObjectDataSource"
SelectedValue="<%# Bind('StatusId') %>" />
</EditItemTemplate>
The SelectedValue="<%# Bind('StatusId') %>"
is what connects up the two datasets so that when you flip a row into Edit mode, the dropdownlist has the correct item already selected, and when you then save it you've got the Status ID to put into your database.
And you're done.