Caution Upgrading from Debian 12 to Debian 13 on machines with mdadm has intermittently failed for me; symptom is that grub EFI is not up to date and system boots into BIOS. Root cause under investigation; it might not be related to mdadm.
To start, read the official release notes.
If your install fits into "vanilla Debian plus maybe a handful of 3rd-party repos", then this guide for a simple upgrade to Debian 13 "trixie" from Debian 12 "bookworm" can be helpful. 3rd-party repos are handled with a find command.
Note upgrade is only supported from Debian 12 to Debian 13. If you are on Debian 11, upgrade to Debian 12 first. Then once on Debian 12, you can upgrade to Debian 13.