Actually it's even simpler than that. If you make sure you have selected "Cloud" instead of "Device" in the Apps screen, everything you have purchased shows up - the ones that need downloaded with a little arrow in the corner of the icon. Just select it and it will download it.
If you don't see it, tap in the upper right corner where the wifi status thing is, then select sync. Give it a few seconds and it should show up.
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