If you use a VGA splitter you will have dual monitor, but both monitors will show the same thing. I believe there is a second option which will enable you to have the dual monitor setup where the computer will see it as a single, large monitor, i.e. if you maximize a window, it will be blown up across the two monitors.
In order to have it so you can see different things on each monitor (a browser in one, something else in the other), you would need either a second video card, or a single video card with 2 video ports. To do this, you would likely also need to upgrade your power supply as there's a good chance you're only running onboard graphics with the emachines and the power supply currently in there wouldn't be recommended to handle a PCI-E GPU.