How to create a trigger that update the date field and time field upon modify of the row?
It would be fairly easy but I would actually recommend changing the logic of the command that is inserting/updating the data so that it adds the additional information at this point. 

However, should you wish to proceed with a trigger you could do something like this:

create trigger my_trigger
on my_table
after insert, update
as
begin
declare @dt datetime = getdate();
update a
set expire_date = CONVERT(DATE, @dt, 101),
    expire_time = CONVERT(TIME, @dt)
from my_table as a
join inserted as b 
on a.product_no = b.product_no; 
end
go  


This uses the INSERTED table to find out the product_no of the rows that have been changed/created. You can find out more about triggers at the link below:

http://msdn.microsoft.com/en-us/library/ms189799.aspx

I hope this helps you.