This repo contains a build script used to build Emacs 28.1 with Debian Bullseye. Copy the script to your cloned emacs directory and run.
This script uses fd, a find replacement written in Rust. Install via cargo, brew, or apt, e.g. sudo apt install fd-find.
To install all the dependencies required to build emacs, run sudo apt build-dep emacs. This will install all the build dependencies for the current emacs package in apt, which should cover most of the dependencies required by the new version of emacs. If after that a dependency is still missing for the new version of emacs, install it as well.