tmux allows you to have multiple panes (the equivalent of windows in Vim) and windows (the equivalent of tabs). To access tmux functionality, you first need to hit a prefix key, followed by a command. The default prefix key is Ctrl + b.
# Use Ctrl- as a prefix.
unbind-key C-b
set -g prefix 'C-'
bind-key 'C-' send-prefix
Restart tmux (or execute Ctrl + b followed by :source-file ~/.tmux.conf) to apply the configuration.
To split the screen vertically, use Ctrl + b followed by %:
# Use - to create vertical splits.
bind - split-window -v
unbind '%'
To create a horizontal split, hit Ctrl + b, followed by ":
# Use | to create horizontal splits.
bind | split-window -h
unbind '"'
You can navigate the panes by using Ctrl + b followed by an arrow key. Every pane operates independently, and you can change directories, execute commands, and (most importantly) use Vim in each one of the panes.
bind h select-pane -L
bind j select-pane -D
bind k select-pane -U
bind l select-pane -R
In the following example, I have a file with some code loaded into the left-hand pane; I'm editing .vimrc in the upper-right pane and listing files with ls in the lower-right pane:
Exit the session by executing exit or hitting Ctrl + d to close the pane.