iPad: export Keynote project to video

Keynote for iOS does not support this. Apparently Apple does not provide any mechanism for screen-recording (video) within iOS 7, and will not permit any third-party app that enables this. There have been some apps that can do screen recording on iOS 7, but they require jailbreaking the device, and are not authorized by Apple through the App Store.

The only way that I know to achieve this is by one of the following:

1) move your Keynote document that you created on iOS to Keynote on Mac OS X, which has a video export feature

2) If you have a Windows PC, you can use Reflector for Windows, which enables live video and audio recording of a "screen share" of what is playing on your iOS device. You establish a connection between your iOS device and your Windows computer, enable "Record" in Reflector, and then play back your Keynote document in full screen on your iOS device. You then have a video on your Windows computer that you can further edit.

One way to do this is to use ScreenSharing on your iPad to a device that accepts AirPlay and then capturing the screen remotely. I have answered a question on this scenario using a Mac with Quicktime and some other AirPlay software here, but I'm guessing you don't have a Mac.

Luckily you can use the software (AirServer) on a PC, so you can airplay mirror your entire screen to your PC, and then use a PC screen capture/recording program in place of Quicktime (You may have to ask another question elsewhere to get a decent recommendation, but a quick google throws up any number of possibilities e.g. here). Although, a quick peek suggests AirServer can now record all by itself on a Mac, with that feature coming to PC soon. That takes a load of complexity out of the task :) Other AirDisplay software is available, especially on Mac, but AirServer is merely the one I am most familiar with that I know does Windows too.

It's not perhaps the most elegant solution, but it's pretty nifty.

Realizing you have a Windows PC without Keynote, and assuming this is a one-time thing you don't need to repeat regularly, I would be happy to convert it for you free of charge if you'd like.