It's worth noting before we start that World of Warcraft is a region locked game. It is available in a variety of regions (EU, US, TW, KR) but if you purchase a copy for another region it will not be compatible with all regions. If your friend is to be playing with his American friends, you will need the US copy if they play on the US servers
According to the various Blizzard sources, in order to gift a copy of World of Warcraft or one of its expansions to a friend you do the following;
Simply add the “Digital Download” version to your cart, and once you complete the online purchasing process, you’ll be given the option to email your game code to a friend as a gift, or -- if you’d rather redeem the code yourself -- have it automatically filled in for you in Battle.net account management.
In order to play the whole of World of Warcraft (ie: get to level 90, explore all of the zones, etc) you will need to purchase all of the expansion packs - only buying the base game will still provide a large amount of content to play, but will prevent your friend from playing any of the maximum level content (or indeed, some of the content before that such as Cataclysm content).
If you need any further assistance with this, or "official" help, I would recommend contacting Blizzard directly.