I know how to do what I need using classic ASP-style coding even in C#. But hoe to achieve the same result with less coding with help of ASP.NET gadgets?

I have form like
<form id="form1" runat="server" ...
and
<asp:SqlDataSource ID="SqlDataSource1" runat="server"...

Problem! How after Insert remain on this inserted record to Edit it?

Maybe lesser problem: how to get unique ID of inserted record? Please don't offer just to select max ID because this is not a correct answer for multiuser app.

Give identity facility Then
In the insert procedure set an output parameter and after insert command
outputparameter=@@identity

To get the unique Id use identity column and in the SP use scope_identity().

Sony

And how do I do that using

<asp:SqlDataSource ID="SqlDataSource1" runat="server"...

?

What the others are saying is that the easiest way is to use a stored procedure to actually insert the record.

Within the stored procedure you can declare a value which can be returned to the asp code

eg Declare @ReturnScope as int

After you have performed the record insertion then in this returned value you place the value in scope_identity()

eg Set @ReturnScope = scope_identity()

Return scope_identity()

When you get back to the asp code then you can use this value to do whatever you want with it.