How To Do An Update On Existing Records?

I have one table of new records (tableA) that may already exist in
tableB. I want to insert these records into tableB with insert if they
don't already exist, or update any existing ones with new data if they
do already exist. A column (Action) in tableA already tells me whether
this is an INSERT, UPDATE, or DELETE. I'm able to derive that I can do
an insert with

select * into tableB from tableA where Action = 'INSERT'

....and I think I can handle the delete.

But I'm stuck on the update. How do I do the update? An ordinary
UPDATE statement just won't do unless I use a cursor to cycle through
the recordset. I want to avoid a cursor.