How can a stowaway hide in the undercarriage?
Wheel wells are deceptively large spaces when the gear is down. It is fully possible to climb up and hide inside one. It's a very different story when the gear is retracted. On many aircraft, the gear doors are  closed when the gear is not in motion, making the space look bigger. 

They are fairly easy to access through the landing gear with a little bit of climbing, or if low enough (like the example below) just jump up into. 



 737 Wheel Well, Petr Volek, from airliners.net

A graphic about a similar event in Hawaii a few months ago:



 From the Independent

Gear stowaways are not new and there have been plenty of occurrences over the years, unfortunately most result in fatalities.


Gear bays are unpressurized, hence normally very cold with air too thin  to sustain life. 
Gear bays are very cramped when the gear is up. If you're in the wrong spot, you will be injured.


It is when the landing gear is lowered (and doors opened) for landing that the fatalities occur, assuming they have not already expired from the environment during the flight. Unable to hold onto the airframe and stay off moving parts they (very gruesomely) fall out minutes away from landing. This is also the story that media often picks up.