Here's how you do it.

If you can use Homebrew, do

Copybrew install docker-compose

and pay heed to the notes after the installer runs. They tell you to add

Copy "cliPluginsExtraDirs": [
     "/opt/homebrew/lib/docker/cli-plugins"
 ]

to your ~/.docker/config.json file.

I don't know if Homebrew also installs Credentials Helper with Compose, so you might have to do:

Copybrew install docker-credential-helper

If you can't use Homebrew, I think you'll have to do the following.

Install Credentials Helper using Docker's instructions here.

Go into ~/.docker/config.json and make sure the value for credsStore is osxkeychain. My file looks like:

Copy{
    "auths": {},
    "credsStore": "osxkeychain",
    "currentContext": "colima",
    "plugins": {
        "debug": {
            "hooks": "exec"
        },
        "scout": {
            "hooks": "pull,buildx build"
        }
    },
    "features": {
        "hooks": "true"
    }
}

Download latest Docker Compose from here for your architecture (aarch64 for Apple Silicon): https://github.com/docker/compose/releases/latest

Copy the executable to /usr/local/bin, naming it docker-compose.

From there, make sure it's executable:

Copysudo chmod +x docker-compose

Clear Apple's scareware:

Copysudo xattr -d com.apple.quarantine docker-compose

As in the Homebrew case, add

Copy "cliPluginsExtraDirs": [
     "/opt/homebrew/lib/docker/cli-plugins"
 ]

to your ~/.docker/config.json file.

Open a new terminal session and try

Copydocker compose version

If that doesn't work, try

Copydocker-compose version

If that works, the cliPluginsExtraDirs entry in the config.json file isn't working.

On my Macbook, I've installed docker via homebrew with

brew install docker docker-compose docker-machine xhyve docker-machine-driver-xhyve

(though this was way before docker desktop became non-free, but I'd assume it'd still work)

This uses xhyve as a virtual machine, so are basically running a Linux distro in xhyve, and then Docker in this Linux distro.

You need to do a bit of configuration, I followed this article.

My commandline for creating the VM was

docker-machine create default --driver xhyve --xhyve-experimental-nfs-share=true --xhyve-disk-size "40000"

docker-compose is now a plugin of the Docker client so it can be runned as docker compose (with a space). This mean that you already have it installed. For confirmation you can try

docker compose version

or even

docker compose

to get a small help page.

The new compose is almost backward compatible with the old one, the differences are described in the official documentation where the old docker-compose is called "Compose V1" and the new one is called "Compose V2".

docker-compose is a utility that is now a parameter in mac docker so instead of docker-compose up, its now docker compose up