The average cost of a horse trainer is $20,000 a year. This amount varies with different institutions offering this service. Check with several people in order to find a perfect deal. You may also get more information at http://www.socalequine.com/atraining/los_angeles.htm.
Depends on what you want the training in and what level of trainer. A fairly local horseman with a decent reputation but not top drawer would run $650-$900 a month (including board). High end trainers would go $1000 and up