Q: How do I buy an iTunes app for a friend

You can send a gift card electronically, or gift an item from the store

http://support.apple.com/kb/HT2736?viewlocale=en_US

Note though that you can only gift within a country as gifts are country and currency specific.  So you cannot gift an app from the USA store to someone in another country.  Nor can you send a gift card in US dollars to someone in Europe as the card will not work there.