Want to download songs to my iPhone; don't want to plug it into the computer
You need to turn on Automatic Downloads in Settings &gt; iTunes &amp; App Store &gt; Automatic Downloads &gt; Music/Apps/Books/Updates in order to get the phone to download anything you buy on the Mac/PC automatically.  You may need to be on a WiFi network, or select the Use Mobile Data option if you are using cell network to download.

In addition, you can also just hop into the iTunes Store on the iPhone, search for the items and then download them manually (you won't be charged again, the Buy option will be replaced with an icon of a cloud with a down arrow), or check your Purchased tab (may be under the More section depending how you have it configured) to list your purchases and have the ability to just show stuff Not on This iPhone.

Alternatively, if you turn on Settings &gt; Music &gt; Show All Music it should show all your purchases inline in the Music App, and allow you to stream or download them at will directly from within the app, but note it will show all purchases, even that Miley Cyrus you are now embarrassed to own...