301 status code on the response.
one-to-one correspondence between legacy urls and new urls for the redirects.
(no "wildcard" redirects to the home page.)
in other words redirect the old home page only to the new domain and 404/410 all other requests;
or, redirect requests for a specific set of legacy urls to the equivalent urls on the new domain and 404/410 all requests for "junk" urls.