You talk to those already IN the kind of job that you want. So whoever is doing this at theme parks or events are your best bet. Join some of the parrot and reptile forums on YahooGroups. Check with the rescues for both those creatures.
It's going to be a very small job field though, you understand, so I would do all I could to get cross training in other lines that would parallel that. Most of which will involve volunteer work. If you're in a large city, check with your local shelters and rescues. It's experience that counts. It won't be a field, though, that will bring in enough money to live on comfortably. Having a 'day job' will be key to following your interest as a trainer/handler on your own time afterwards.
Be aware that you can supplement this interest by WRITING about it, if you have writing skills. As articles or short stories or even a full book for publication.
If you can find a used copy on Amazon of 101 Best Businesses For Pet Lovers, get it, it's got some good ideas in it.
There are online links you can check ----
https://www.glassdoor.com/Salaries/animal-trainer-salary-SRCH_KO0,14.htm
https://www.salaryexpert.com/salary/job/bird-keeper/united-states
http://betterwords.typepad.com/birdvice/2009/01/careers-in-birds.html