(Note: this post is a wiki; anyone Trust Level 1 or higher on the forum can edit and improve it.)
A Bit of History
The current ACME standard is documented in RFC 8555. Information specific to Let's Encrypt can be found in the ACME Protocol Updates page of the documentation. If you're writing your own client, you may need to refer to those documents, but most people use a client that has already been written.
If you use Certbot (as a lot of people do when managing their own servers), please see this thread for information on upgrading:
CPanel, LiveConfig, or other hosted solutions
If you don't have access to a shell for your web site (that is, you only have a web-based management interface such as CPanel or LiveConfig and can't SSH or otherwise run commands on your web server), and you can no longer get certificates due to getting an error that ACMEv1 is deprecated, your web hoster needs to upgrade the version of their management software.
(If you are the web hoster and need help upgrading your management software so that your users can continue using Let's Encrypt, please feel free to ask for help in this forum and we'll do what we can, but you may find working with the provider of your management software to be more helpful as they are probably more familiar with the details of upgrading.)
(This software is also known as Windows ACME Simple or WACS, older versions were known as letsencrypt-win-simple or LEWS.)
You need to be on at least version 2 of win-acme to handle the current ACME standard. See its web site for information on upgrading and migration steps:
Certify The Web
Certify v3.x and lower must be upgraded. If you're seeing something like this:
Could not begin authorization for domain with Let's Encrypt: YourDomainNameHere
or any other error, you should download and install the latest version from https://certifytheweb.com/. If you need further assistance, you can ask in this community or in the dedicated support community for Certify The Web at https://community.certifytheweb.com/.
Selecting a New ACME Client
If you use a client or library that is no longer under development and thus doesn't have support for the current ACME standard, you need to change to using a different client or library that does. While there is a list of ACME clients from which to choose, you may benefit from asking for advice in this community about selecting a client that fits your needs. There may be other clients not listed that could work very well for you based on your circumstances.