Get Creature Management 3 first so that you can have 2 pets out and be able to train the (very useful) “Group” and “Follow Other” commands. Next go up the Creature Taming line to be able to handle the more aggressive creatures, followed by the Creature Training line to store more pets, then finally the Creature Empathy line.
Gained by taming a wild creature, training pets new commands, and by having your pets kill MOBs.
Grab some Pet Stimpacks Cs or Ds and have your pets fight some higher-level mobs is the standard way to gain CH XP. However, in order to gain CH XP for having your pet kill a MOB your pet only has to hit it once before it dies, so you should do most of the damage yourself and only send the pet in to attack when the MOB is almost dead.
Use low-level pets to gain XP faster. Remember that the CH XP gained when killing MOBs is determined on your pet’s level compared to the MOB’s level. Babies work well, but even their level for gaining XP is not determined by their current level, when CH XP is concerned it is never considered to be lower than half of what their adult level will be. Keep this in mind. In fact, the best pets to use are Bio-Engineered specialized creatures with high Kinetic defenses (max 60%) and a strong attack, but with a low level. You can get some pretty powerful CL12 pets from a good BE.
To have your pets effectively track and attack a target don’t just use the “Attack” command, use the “Follow Other” command first and then the “Attack” command when they reach their target.
While there is now a supplied Tame macro the following macro will help immensely when taming wild creatures. Basically, if the target begins attacking, you will not attack back, giving you the chance to run away and try again. Also, if you were to attack the target all of its social friends around would begin attacking you too, leading to a messy situations and potentially a lost future pet.
Another advantage to Bio-Engineered creatures is that they will always learn a new command on the first attempt and always give 100 CH XP, greatly reducing the training time and thus increasing the rate of XP gained. A good strategy is to find a BE grinding their sampling line and get them to create you creatures for training. They will likely be collecting lots of garbage DNA Samples that they would otherwise destroy. Just train the creature all available commands and release it.
Optional: Get some clothes with Bio-Engineer enhancements for Taming Wild/Vicious Creatures and Mask Scent. Be aware that the highest that each of these bonuses can accumulate is +25 (even though it will add up higher, it will only count up to the +25).