AToW (at least my printing, the 1st - but I checked the errata and found nothing) is a bit of mess as far as learning skills in gameplay is concerned - including those definining a mechwarrior, Piloting and Gunnery.
First of all, AToW is adamant (p.159 and 334) about the fact that you can't possibly improve advanced skills without a trainer who's strictly better than you. So, in the Battletech universe, there are no Mechwarriors with Veteran, or even Regular, Piloting or Gunnery skill levels - otherwise, who could have trained the first Mechwarrior who reached those skill levels (since nobody before him had them, so nobody could have trained him)? It doesn't matter how many mechs you've downed in battle, if you can't get lessons you'll stay evergreen.
One thing about which it AToW is not adamant, however, is how much training you need, and how much it benefits you. p.159 suggests that you need a week to train in any skill. On the other hand, p.334 says that, as a guideline, you might need 1 week for a basic skill, 1 month for an advanced one, double or halved for Slow/Fast learner, doubled or halved for Poor/Excellent training facilities. Also, p.159 says a week of training in a skill nets you 2xp (for a basic skill) or 1xp (for an advanced skill), times the MoS of the trainer in his Training skill check, modified by the INT linked-skill bonus of the student (+1 for 7-9, -1 for 2-3 etc.), in addition to the "right" to improve the skill if advanced. On the other hand, p.334 says that for a week of dedicated study (for a basic skill) or a month of dedicated study (for an advanced skill) you just get the MoS (unmodified by the INT of the student) and the "right" to improve the skill if advanced, or the full INT of the student plus the MoS, without the "right" to advance the skill unless it's basic.
So, how are you playing it? And how do you solve the "trainers required for advanced skills" problem?