SSH (secure shell) opens a terminal on another machine over an encrypted connection. It's how almost every Linux server is run.
$ ssh sam@203.0.113.20
sam@server:~$ hostname
server
sam@server:~$ exit
Passwords work, but keys are safer and quicker. A key pair is two files: a private key that never leaves your computer, and a public key you put on each server. Make a pair once with ssh-keygen -t ed25519; the files go in ~/.ssh/. Then ssh-copy-id sam@203.0.113.20 installs the public key on the server, in ~/.ssh/authorized_keys, and from then on you log in without the password.
Keep the private key private: the .ssh folder should be 700 and the key 600, and SSH refuses to use a key that others can read. Give it a passphrase so a stolen laptop doesn't mean a stolen key.
To copy files, scp file.txt sam@server:/tmp/ sends one across (swap the order to fetch), and rsync -av site/ sam@server:/var/www/site/ copies a folder and, next time, only what changed.
Once keys work, harden the server in /etc/ssh/sshd_config: PasswordAuthentication no stops password guessing, and PermitRootLogin no stops anyone logging in straight as root. Restart the SSH service, and keep your current session open while you test a new login in a second window, so a mistake can't lock you out.
Short names save typing. In ~/.ssh/config on your computer, a block like Host web with HostName 203.0.113.20 and User sam lets you just type ssh web.