How to split the terminal into more than one "view"?

You can do it in screen the terminal multiplexer.

• To split vertically: ctrla then |.
• To split horizontally: ctrla then S (uppercase 's').
• To unsplit: ctrla then Q (uppercase 'q').
• To switch from one to the other: ctrla then tab

Note: After splitting, you need to go into the new region and start a new session via ctrla then c before you can use that area.

EDIT, basic screen usage:

• New terminal: ctrla then c.
• Next terminal: ctrla then space.
• Previous terminal: ctrla then backspace.
• N'th terminal ctrla then [n]. (works for n∈{0,1…9})
• Switch between terminals using list: ctrla then " (useful when more than 10 terminals)
• Send ctrla to the underlying terminal ctrla then a.

Try tmux (Terminal MUltipleXer):

• Home Page
• Wikipedia

And to understand the difference between session, window and pane:

As mentioned in the comments, besides screen, another good terminal multiplexer is tmux. You can refer to the manual for a complete description and command reference. Some basic operations to get started are:

• Split screen vertically: Ctrlb and Shift5
• Split screen horizontally: Ctrlb and Shift"
• Toggle between panes: Ctrlb and o
• Close current pane: Ctrlb and x

You can achieve more complex layouts by splitting panes. You can also have multiple windows with panes and switch between them.

• Create windows: Ctrlb and c
• Switch to next window: Ctrlb and n
• Switch to previous window: Ctrlb and p
• Destroy current window: Ctrlb and Shift7