I bought a song on iTunes on my iPad, but the song is greyed out. How can I get the song back?
Also, how can I download the song to my iPad or iPhone?
I believe if the song is present on your iPad/iPhone library it will be grayed out in iTunes (on iOS) probably the purchased playlist?
In regards to that downloading again without repurchasing, ONLY applications purchased can be re-downloaded for free without repurchasing. Songs and audiobooks require you to re-purchase. This is because the record companies have explicitly stated this in their agreement to Apple. Whoever told you that information was wrong.
However, if you email Apple, you can request to restore all downloads. This means everything you bought will be available for download again (except some that have changed name or have been removed from iTunes store) but do note that this can be used one time only. It's for people who had their laptop stolen and lost everything or a broken hard drive with loss of data.
Hope that clears things up.
As of the release of iTunes in the Cloud, it has become much easier to re-acquire media that was previously purchased from iTunes.
With regard to the question, there is now a Purchased tab in the iTunes app on iOS, which allows you to find and re-download any song, movie, tv show, or book that you have previously purchased with your iTunes account on any device.
It is worth noting that this feature may not be available in all countries, or that the availability of any given piece of media may differ between countries (up until recently, one could only re-download music and TV in Canada, for example, but not movies).