Coldfusion upgrade

That's a lot of guidance you're asking for. You haven't described your environment at all. I recommend you migrate one or two apps to the new environment and see what happens. I wouldn't recommend running both old and new on the same server. You can use the 30-day trial version of CF. This will give you an idea how much the whole migration would cost. CF is pretty good with backward compatibility but again, you haven't described your current environment. @Charlie Arehart is a competent consultant to help you migrate.

Dave Watts, Eidolon LLC 

It would help to know what aspects of the process you want to know more about, as there are many:

1. Are you asking about cost and licensing details?
2.  Are you asking about installation, such as finding and choosing among alternative ways to do that? 
3. Are you asking about migration of cf admin and jvm config settings? 
4. Are you contemplating moving cf from an old OS to a new one? Same with the database you'd be talking to? 
5. Are you contemplating moving from one architecture to another, like from a single local server to a VM or the cloud or containers? Or would you want to try to run the old and new cf on a single server?
6. Are you asking about migration of cfml code, and about what compatibility issues to anticipate?  And are you moving to cf2021 or the new cf2023 released this month? 
7. Are you asking about what's changed in cf and cfml since then, including what new things you might take advantage of? 

Even if you answered yes to each of these, it would help then to know how much you already know about the topic, since much could be said on each. Indeed, are you a cf developer, cf administrator, business person, or some other role? Each topic will have levels of detail more appropriate to each such role.

It should be obvious by now that there's no simple single "direction" that can be offered, let alone a single "process". Others may well offer a simpler answer for you, and if that may suffice then great.

But as I've helped people make such migrations several and address such issues hundred times, I can say it's not difficult to do but there's much that needs to be understood to do the job effectively. I can point you to several presentations I've given and blog posts I've written, on nearly each of those topics above. You can just look at carehart.org/presentations or /blog to review them, or once we know your replies to the above I should be able to point to specific ones.

Finally, if you just want help to "get it done" in a matter of hours, getting each of the above addressed to your/ your team's specific interests, experience, and situation, I'll add that I can offer that help, remotely, with satisfaction guaranteed (you won't pay for time you don't find valuable). I don't just "do it all" for you but instead help you do it. If you have developers who could test and implement needed code or configuration  changes, I'm saying I could help them do all that more effectively than if they worked entirely on their own or with help from the community.

I've helped most get such a migration done in a matter of hours or days, where on their own it could have taken (or they feared it would take) weeks or months. For more on my rates, approach, online calendar link, and more, see carehart.org/consulting. 

Still, I realize some have "no budget" and must (or just prefer to) do everything themselves. Again, I offer those many resources above to help them. And if you clarify those things above, I or others may be better able to help you directly here.