There are Insert, Update, Delete and Instead of Triggers. You will want to create an Insert, Update and Delete triggers for your purpose.
Here's a short example:
create trigger mytable_del on mytable
for delete
as
declare @stuff
insert something into mytable_audit
where something and something else
end
go
Here's the documentation. If you have problems with specific parts of your triggers, then you can post those specific code questions here, but it's unlikely that someone here will write your triggers for you.