How do I get into a Docker container’s shell?

docker attach will let you connect to your Docker container, but this isn’t really the same thing as ssh. If your container is running a webserver, for example, docker attach will probably connect you to the stdout of the web server process. It won’t necessarily give you a shell.
The docker exec command is probably what you are looking for; this will let you run arbitrary commands inside an existing container. For example:
docker exec -it bash

Of course, whatever command you are running must exist in the container filesystem.
In the above command is the name or ID of the target container. It doesn’t matter whether or not you’re using docker compose; just run docker ps and use either the ID (a hexadecimal string displayed in the first column) or the name (displayed in the final column). E.g., given:
$ docker ps
d2d4a89aaee9 larsks/mini-httpd “mini_httpd -d /cont 7 days ago Up 7 days web

I can run:
$ docker exec -it web ip addr
1: lo: mtu 65536 qdisc noqueue state UNKNOWN
link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00
inet 127.0.0.1/8 scope host lo
valid_lft forever preferred_lft forever
inet6 ::1/128 scope host
valid_lft forever preferred_lft forever
18: eth0: mtu 1500 qdisc noqueue state UP
link/ether 02:42:ac:11:00:03 brd ff:ff:ff:ff:ff:ff
inet 172.17.0.3/16 scope global eth0
valid_lft forever preferred_lft forever
inet6 fe80::42:acff:fe11:3/64 scope link
valid_lft forever preferred_lft forever

I could accomplish the same thing by running:
$ docker exec -it d2d4a89aaee9 ip addr

Similarly, I could start a shell in the container;
$ docker exec -it web sh
/ # echo This is inside the container.
This is inside the container.
/ # exit
$

To bash into a running container, type this:
docker exec -t -i container_name /bin/bash

or
docker exec -ti container_name /bin/bash

or
docker exec -ti container_name sh