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SELECT * FROM INSERTED or even better:
insert into HC_Audit
(User_ID,System_Time,Affec
SELECT User_ID,System_Time,Affect
assuming the tables have identical structure.
For DELETE is the same just replace INSERTED with DELETED - these are internal SQL tables used during the standard DML operations.
For UPDATE is a bit more tricky as an UPDATE is done in SQL like a INSERT and DELETE so the INSERTED table in a update trigger will have all NEW values going in that row(s) and the DELETED table will have all the OLD values that were updated by the new values coming from INSERTED.
Based on this you can chose to log both operations and keep old/new values for an update.
I also suggest in your Audit table to add a TriggerAction column for instance to be able to tell what operation was logged - Insert/Delete/Update or...you can have one table for each of them but that would mean three audit tables for 1 parent.
"Using the inserted and deleted Tables"
http://technet.microsoft.com/en-us/library/ms191300(v=sql.100).aspx
http://www.mssqltips.com/sqlservertip/2342/understanding-sql-server-inserted-and-deleted-tables-for-dml-triggers/