The first step is to qualify and begin practise as a lawyer. The second is to decide which area of 'aviation law' you seek to specialise in. I put it in inverted commas, because the subject is very wide and ill-defined. In reality, aviation law encompasses subject matter varying from criminal law (pilot prosecutions) to international law (treaties), competition law to insurance law. You get the point! It is difficult to become an expert in all of these fields.
I would suggest aiming for a position with a large city firm that acts for one of the major carriers, or alternatively aim yourself at an in-house airline legal team. My experience is that there are scraps of aviation work about, mixed with similar work from other clients, unless perhaps you were to train and set yourself up as a barrister specialising in the criminal side. However it takes a while to build a good reputation if that is the path you decide to follow.
There are good specialist post graduate aviation degrees available, for instance from McGill in Montreal. Check out the options.
A healthy interest in aviation, pilot experience etc will also stand you in good stead for the future. You may find out, as I ultimately did, that you would rather fly the aircraft than represent the airlines.
Good Luck.
T.