Can you order a mp3 song from amazon and put it on your iphone library?

I have a wish list of a couple of mp3 songs on amazon. Once I buy them, would they appear in my iTunes library on my laptop? If not, is there a way to get the mp3 songs into my library. I haven't gotten the amazon cloud player yet because most of the reviews kept say they were still having problems after the recent update.

Music you download doesn't just "appear" in your iTunes library. You drag it there with your mouse from whatever folder it downloaded it to into the iTunes window. You don't have to have it in iTunes to put it on your iPod. You can drag it from wherever the file is onto the iPhone tab on sidebar (ctrl s if you don't see it).

Many people will say "sync" - which is one way of putting music on an iPod or IPhone. That's actually the stupid way of doing it. The better way is setting the iPhone to be manually managed for music and video. No jailbreak needed - you can do that in iTunes on your computer when your iPhone is connected. I've been doing it that way for years and have never had the problems that other iPod or iPhone users have.

Manual Management works on every Apple device I've ever used - different generations of ipod nano and Touch, iPhone and iPad, including those using iOS 7.

Yes, I use only MP3 on my iphone. See: http://www.gatorspit.com/tips/itunes-mp3.html