TOPIC:

I own the old domain name and the new one. Went through the process of specifying in FTH settings the new domain name. Seems to have succeeded.
If you type in the new name, our site comes up. However, if you do a Google search for our new club name, the old domain name (defunct) comes up and if you hit that, it takes you to FTH site.
I went through the arduous process of proving to Google Search Console that I own the old domain name.
Now I am in the instructions for using the Change of Address Tool:
support.google.com/webmasters/answer/83106?hl=en
On that page, it says, cryptically:
If you do not first set up 301-redirect directives, your change of address request will not work.
Google searching for "how do i set up 301-redirect directives" brings up discussion of doing this in Apache. What the heck. .
I am non-techie and could use guidance. Thank you,

1) we do not support redirects of any kind

2) if you make a change in your domain don't forget to change all the places on the web where your old domain is. Like your district website, toastmasters.org find a club.

3) it can take google 1 to 6 months to spyder a website so the old domain disappears from the sear results and the new domain shows.

Not being technically savvy, I would like more information. When you say " we do not support redirects of any kind," I interpret the "of any kind" to imply that redirects per se are regarded as somehow bad. Can you explain, since Google regards this step as required?
Or, when you say "we don't support," do you mean "that kind of thing is not our focus -- we are concerned with other, more important matters such as X and Y. . ."
The meaning of your statement may be obvious to you but I don't have the same background, so would you explain, please?