Travelling with a cello 101 : The extra seat and the airlines...
Booking your ticket and the cello's ticket :
Option 1 : Booking a real EXTRA SEAT*
*An EXTRA SEAT is like an extension of your own seat, it is exempt of airport taxes, but has to be booked by phone as "Special Service Request". (For low cost companies , they often tell you to buy 2 seats, then go to option 2.)
Option 2 : Booking 2 full seats
And then : Installing your cello on board
Everything is explained here: http://www.thepracticehelper.com/cbbgcello.html