Start here: https://code.google.com/p/android-x86/downloads/list . Android ISO images, grab android-x86-4.3-20130725.iso. Note that this is version 4.3 - a bit behind the curve, and they don't seem to have a newer version available. This can be used as a live disc, or as an install disc. Most Linux ISOs do both, but this one has two separate boot options, one to install, the other to test live. To install, you'll need to be familiar with Linux installation steps, particularly the use of cfdisk.
VirtualBox's behaviour toward this guest OS seems to vary by the host OS, or at least it did for me. Under Windows it worked fine, although there's no Guest Additions and so no pointer integration - you'll have to press the Host Key to break the mouse out of the guest OS. But under Linux I had pointer integration ... and couldn't see the pointer at all. This turns out to be because under Windows VirtualBox chose a different mouse setting. VirtualBox -> Settings -> System -> Mouse Pointer: change from "Tablet" to "PS/2 mouse" ( https://forums.virtualbox.org/viewtopic.php?f=6&t=16255 )
You'll find that Android frequently goes black, and key-presses won't bring it back. Keep in mind that it thinks it's a phone/tablet, and this is S.O.P. To wake it back up, you need to do the equivalent of pressing the power button. Use VirtualBox -> Machine -> ACPI Shutdown, or remember that the shortcut for that action is Host-Key-H.
Researching the disappearance of the pointer led me to a couple other points that aren't essential to getting the Android guest running, but are likely to prove useful: to activate Developer features, go to Android -> Settings -> About Tablet -> Build Number, and tap on Build Number seven times (really). This apparently varies by Android version, but works in the ISO build we're discussing. ( http://www.ninjaromeo.com/enable-usb-debugging-developer-options-jelly-bean/ )
Information about showing the pointer in Android: http://stackoverflow.com/questions/10233537/how-to-show-on-screen-the-cursor-position-on-an-android-tablet-or-smartphone - note that this is less useful than it sounds in VirtualBox unless you're doing development as it only shows the pointer position when the mouse button is held down.
A couple important questions, at least from my point of view:
(1) is it possible to change the orientation or the resolution of the instance? (It appears to be locked at 1024x768 horizontal) [ to investigate: http://twigstechtips.blogspot.ca/2013/02/android-x86-how-to-change-screen.html ]
(2) can the instance be rooted? It can still be used for testing, but it's of considerably less use for development if it can't be rooted ... [ to investigate: http://forum.xda-developers.com/showthread.php?t=2390619 ] Also, Alt-F1 gets you to a text-based root terminal (Alt-F7 gets you back). Linux convention suggests that we might also have consoles on Alt-F2, Alt-F3, etc., but that doesn't seem to be the case.