Question: What program or system utility can I use to convert my desktop into two work areas using a single monitor?

*Some recommendations for an easy to use application?*

Answer: 
It's called workspaces and if you're running plain old vanilla Ubuntu with Unity, go the to gear icon in the top left of your screen:

[![Gear Icon](https://i.stack.imgur.com/uxEAW.png)](https://i.stack.imgur.com/uxEAW.png)

then go to:

* `System Settings`
* `Appearance`
* the `Behaviour` tab
* `Enable Workspaces`

and then press the workspace switcher icon:

[![Workspace switcher](https://i.stack.imgur.com/cp0n2.png)](https://i.stack.imgur.com/cp0n2.png)

and be amazed:

[![Screenshot 4 workspaces](https://i.stack.imgur.com/9UVL9.jpg)](https://i.stack.imgur.com/9UVL9.jpg)

**Note:** Pressing `Super`+`S`¹ accomplishes the same thing.

¹`Super`+`S` is aka `Windows`+`S`
I agree with the posted answers; they're the right answers. But there's another option in stock Ubuntu that runs Unity (e.g. 14.04, but not 16.04+) that satisfies one interpretation of the question, and can generally be handy to know

You can easily resize windows to take up half or a quarter of the screen. You can do this with `Ctrl`+`Alt`+**any number on the num pad** (in number mode). This will resize the current window as follows:

* `ctrl`+`alt` + ...
* `1`: top left
* `2`: bottom half, full-width
* `3`: bottom left
* `4`: left half, full-height
* `5`: full screen
* `6`: right half, full-height
* `7`: top left quarter
* `8`: top half, full-width
* `9`: top right quarter
* `0`: minimize window (I've remapped this to make windows take the full vertical screen height, keeping the current width)

So with one window do `Ctrl`+`Alt`+`4`, and with the other `Ctrl`+`Alt`+`6`, you'll have the screen split into two halves temporarily.