I used to use screen on my AWS EC2 Linux instances. Moving forward after my recent demo install of Ubuntu Server 14.04 LTS, I'm going to be using tmux from now on. I'll even try tmux if I ever need to work in an older server instance which has been temporarily regenerated from archived snapshots--as long as tmux is already available in the relevant package repository for that older OS.
Here's how I first start it from inside the server...
ubuntu@ip-10-238-243-18:~$ tmux new -s session-name-1
However, I don't really need to login to that remote just to do this. I can start tmux from my local terminal...
reg$ ssh -t ubuntu@54.147.55.37 "tmux new -s session-name-1"
And here's what the new tmux session looks like
Nothing seems different! But then if I want to, for example, reference a man page and keep it in view, I can split the window into 2 panes. First type in the prefix key, which is CTRL-b by default (screen used CTRL-a, remember?), then type " to split top and bottom.
<CTRL-b><">
Then, I'll switch back to the upper pane to be the active pane, by typing <CTRL-b><UP-arrow>. I now want to split this pane into left and right, so I'll type <CTRL-b><%>.
I can then detach from this session so that it will continue running on the remote server, independent of the operational status of my local computer. Type <CTRL-b><d>, then logout of the SSH session using exit or <CTRL-d>.
To resume a remotely-running tmux session, I can type the following directly from my local terminal...
reg$ ssh -t ubuntu@54.147.55.37 "tmux attach -t session-name-1"
... and my remote stuff is running just as I left it!