You can now safely logoff from the remote machine, your process will keep running inside tmux. When you come back again and want to check the status of your process you can use tmux attach to attach to your tmux session.
If you want to have multiple session running side-by-side you should name each session using Ctrl-B and $. You can get a list of the currently running sessions using tmux list-sessions.
Ctrl-b c Create new window Ctrl-b d Detach current client Ctrl-b l Move to previously selected window Ctrl-b n Move to the next window Ctrl-b p Move to the previous window Ctrl-b $num Move to window $num Ctrl-b w list windows Ctrl-b & Kill the current window Ctrl-b ! close other panes except the current one Ctrl-b , Rename the current window Ctrl-b % Split the current window into two panes Ctrl-b " split pane horizontally Ctrl+b arrow key - switch pane. Hold Ctrl+b, don't release it and hold one of the arrow keys - resize pane. Ctrl-b q Show pane numbers (used to switch between panes) Ctrl-b o Switch to the next pane Ctrl-b ? List all keybindings Ctrl-b x exit Ctrl-b s list sessions tmux new-session start a new session tmux attach re-attach a detached session Ctrl-b :detach detach from currently attached session