I've been using byobu, which is a wrapper. No idea how actual screen or tmux work, but in byobu it's just F2 for a new screen, F3 for previous, F4 for next, ^A, D to disconnect. And ^A, & to kill a screen. Those are the only commands I've ever needed.

I should probably learn how to actually split a terminal, but I've never been in a situation that I couldn't just move the terminal emulator window.