How to automatically run commands on SSH login?

Put the commands in ~/.bashrc. Anything in there is executed each time you log in.

If you need commands to only run when logging in via ssh (but not when logging in physically), you could probably test for the presence of the SSH_CONNECTION environment variable, and only run the commands if you find it exists.

Just put this in ~/.bashrc or /etc/bash.bashrc if you want this for all users:

if [[ -n $SSH_CONNECTION ]] ; then
    echo "I'm logged in remotely"
fi

Alternatively, you can specify a command to be run during the invocation of ssh:

$ ssh -t server 'cmd; exec bash -l'

The last command in the list should start an interactive session in your preferred shell. If you have a lot of commands to run, consider creating a script file on your SSH server.