Generally, your pets will start out with poor stats. But not to worry! You can always train them and make them better fighters. But before we start, here is a quick rundown of what everything is: (I put a * next to the things I recommend training.)
*Level: This is key to training at the training schools because the amount of strength, endurance, agility, and defence you can train relies heavily on your pets level. Which faerie abilities you can give your pet is also dependent on their level.
*Hp: This is your pets hit points, or amount of damage he/she can take in the battledome. In the training schools, this is often referred to as "endurance", but we'll get to that later.
*Strength: This determines the amount of damage your pet can inflict. A high strength wont do damage without weapons though! Also, it only comes into play if you do "fierce attack", "jump and attack", "normal attack", or "cautious attack".
*Defence: This determines how well your pet can defend him/herself from attack. It only comes into play if you do "defend".
Movement: This doesn't do anything. It is also referred to as "agility" in the training school, so don't get confused. Don't bother to train this one, either.
Intelligence: This doesn't affect your pet in the battledome.
You got all that? Now we can move onto the actual training methods!
Coltzan's Shrine: Coltzan's shrine is random, random, random. It's free though! It improves: level, strength, defence, and movement. It also might give out random items ranging from burnt food to a dubloon coin, heal your pet, fill your pet up with food, or do nothing. It is located in the lost desert, and you can go once per day. Even if it's free, and I definitely recommend going, it isn't *really* a training method. If you want to be serious, try some of the other methods.
The Krawk Island Academy: This my personal favorite because a) it's cheaper than the mystery island training school b) you can train your pets for free on their pet days and c) you can withdraw from a class if you don't want to pay. The swashbuckling academy trains all of the stats listed above (except intelligence, which isn't even a battledome stat), but will only train your pet up to level 40. You pay in dubloons.
Mystery Island Training School: This is more expensive than the Krawk Island training school, BUT it trains your pets twice as fast and you can train here up to level 250. (It trains all of the same stats, too.) It is located on Mystery Island and you pay for your classes in codestones.
Secret Ninja Training Schol: If you're training your pets here, then you know you are a serious battler. You can only train your pets if they are over level 250, and you have to pay in the rare red codestones. It is a hidden link on mystery island, go to Belle's page if you want to know how to get there.
The Secret Lab Map: Warning! This is an extremely risky way to train your pet, it is completely random, and I take no responsibility whatsoever for what happens! The labray can (and will, if you do it long enough) change your pet's gender, change your pet's species, and/or change your pet's color. It might even make your pets stats go down! But more on that later. You have to buy all nine pieces of the secret lab map (item: Secret Laboratory Map) before you can use it. Prices generally range from 50,000 np to 60,000 np, so it might take a while to save up. In the long run, it saves np because you don't have to cough up np for codestones, dubloons, etc. (I don't recommend doing this AND training normally, by the way...) and because it might paint your pet a rare color. Some colors, in fact, are only available from the secret lab map! Here's the catch. The labray may improve your pet's level, endurance, strength, defence, and agility, but there is also a chance (a smaller one than them improving) that it will decrease your pet's level, strength, defence, and agility. It never lessens hp though, so no need to worry on that count! You can get to the secret lab map through games - puzzles - treasure maps - laboratory. Once you have the map, you can use it once a day forever and ever. If you want to know more, I recommend going to JustToClearThingsUp's petpage. Disclaimer! I am in no way responsible for the contents of this petpage! I did not make it!