A: Certifying my cats as ESAs was very easy, actually. I have talked to my own counselor about my cats and the benefits I get from owning them; so he readily agreed to write a letter explaining that the cats are ESAs who help a person with a disability. That letter--from a doctor or from a psychologist--is really all you need. Legally, having a pet is an accommodation that you as a disabled person can request from a landlord; and this is part of the laws that require not discriminating against disabled tenants. So, what you would need to do is talk to your counselor and explain your problem, get them to write a letter explaining that your cat offers emotional support, and take that to your landlord.
Now, you have responsibilities, too. While an emotional support animal does not have to be trained to behave politely in public as a service animal might, the ESA must be non-disruptive, non-destructive, and generally well-behaved. If the animal damages anything, you are responsible to pay for repairs, as any tenant with a pet would be. The animal cannot disturb the neighbors. If you haven't already had your cat spayed, I recommend you do that; during her heat cycles, she will tend to become noisy and attempt to escape--this is dangerous for her and annoying for the neighbors, and if she gets out, you don't want to be dealing with kittens. Call the humane society in your area and ask if they subsidize low-cost spay/neuter. You can often find vets who will alter pets at cost (i.e., you pay what it costs them to do the operation only); they know how many kittens are euthanized in shelters and they don't like it one bit. You'll have to make sure she is using the litter box and scratching post appropriately, and that she is either collared or microchipped so that she can be recovered if she darts out the door.
I've found some links which might be helpful to you. Of course, you should do your own research as well.
Service Dog Central
Emotional Support Animals
Wikipedia article (Check the references)
As for approaching your landlord, don't start out confrontational. As a landlord, their fear is likely to be that your cat will be either destructive or annoying to the neighbors, and they will tend to be reassured that the law protects their property by allowing the landlord to require you to pay for any damages just as you would for a normal pet. They may also believe that your ownership of a cat will inspire other tenants, who do not need ESAs and might not be responsible pet owners, to obtain cats for themselves. Explaining that your cat will be in your apartment at all times, and will not be let out, may be useful here. Of course they will want to see the letter. In my case, my landlord was very good about it, and didn't even bother with the letter except for my filing it along with my application.
Some landlords will ask you to declaw your cat. Obviously, you don't want to do this; it's unnecessary and cats need their claws. You can usually get around that by using claw caps like Soft Paws, though most owners do just fine with simply providing the cat a scratching post or pad (or two, or four), and possibly luring the cats to the scratching surfaces with catnip. I have two posts and two cardboard scratch pads in my one-bedroom apartment and I partly credit them for my cats' thus far failing to cause any damage whatsoever.
If you are really worried that the conversation may become awkward or hostile, there is nothing wrong with bringing a friend along with you when you go to explain things to your landlord.
Good luck to you and your cat. I know how helpful it can be to have an animal around, and I wish ESAs were more widely accepted and recommended. After all, it's a much nicer treatment to have a cat than to take a pill, because pills don't purr and cats don't stick in your throat and taste bitter!