Please remember that we cannot offer legal advice here. These are the steps others have used with success. They may work for you too or they may not. If you need legal advice on your specific situation, you should consult a qualified attorney.
1. Get a prescription from your doctor.
Consult a doctor for an evaluation on whether you have an impairment that substantially limits one or more major life activities. Ask the doctor if he or she believes the presence of an emotional support animal would be necessary for your mental health. If the doctor believes you are disabled and you need an emotional support animal (ESA), ask him/her to write a letter addressed to your landlord to that effect or to write you a prescription for an emotional support animal.
2. Print out the Bazelon article Fair Housing Information Sheet # 6 Right to Emotional Support Animals in "No Pet" Housing
3. Write a "request for accommodation" letter
4. Send a copy of the prescription and the Brazelon info sheet, along with your letter, to the landlord. Send this CERTIFIED, RETURN RECEIPT.
5. Assuming you have already spoken with your landlord and been denied, do not speak to the landlord informally about this again. Insist that all discussion on the matter be by mail or email (so you have a record of who said what and when).
These steps resolve the issue for most people. If it does not work for you, consider filing a complaint with HUD or hiring an attorney to file a civil suit against the landlord.
Consider carefully how filing suit might effect your relationship with your landlord. It may be healthier to find a different place to live that is more accepting of ESAs.
Most people who have filed suit have reported that whether they win or not the experience was the most stressful event of their lives.