There is no need to download a Yahoo Messenger app on your mobile phone. Just go to the browser of your mobile phone and type m.yahoo.com/messenger to start using Yahoo Messenger.
However, if you want to download the application on your Apple device, go to App Store on Home screen. Tap on Search and type Yahoo Messenger. Tap Install, you will be required to enter your iTunes Store account information.
If you want to know how to download Yahoo Messenger on your Android phone, just go to the Android Market on your phone. Type on the search box "Yahoo Messenger". Click on "Install" to download the app.