Since March 15, 2012, ADA compliance with the 2010 Standards will be required for new construction and alterations. In the period between September 15, 2010 and March 15, 2012, covered entities may choose between the 1991 Standards ADA Compliance (without the elevator exemption for Title II facilities), the Uniform Federal Accessibility Standards (Title II facilities only), and the 2010 Standards ADA Compliance.
Two agencies within the U.S. Department of Labor enforce parts of the ADA. The Office of Federal Contract Compliance Programs (OFCCP) has coordinating authority under the employment-related provisions of the ADA. The Civil Rights Center (CRC) is responsible for enforcing Title II of the ADA as it applies to the labor- and workforce-related practices of state and local governments and other public entities. Visit the Laws & Regulations subtopic for specific information on these provisions.
As a result, most ADA suits are brought by a small number of private plaintiffs who view themselves as champions of the disabled. For the ADA to yield its promise of equal access for the disabled, it may indeed be necessary and desirable for committed individuals to bring serial litigation advancing the time when public accommodations will be compliant with the ADA."
Most recently, however, pizza chain Domino's has been brought under suit for their website not being accessible for specialty ordering. The U.S. Supreme Court refused to review the case, instead upholding the decision of the 9th U.S. Circuit Court of Appeals who said the “alleged inaccessibility of Domino’s website and app impedes access to the goods and services of its physical pizza franchises—which are places of public accommodation.”
ADA compliance isn’t a set-it-and-forget-it thing. Compliance standards must be followed and will evolve just as your website does. There are guidelines all website contributors must know to stay within ADA guidelines. It is generally not burdensome but it does require some web managers to change their workflows. For example, loading images up to your ecommerce site will always need some of that alternative text (alt tags) mentioned above.
Another federal agency, the Architectural and Transportation Barriers Compliance Board (ATBCB), also known as the Access Board, issues guidelines to ensure that buildings, facilities and transit vehicles are accessible to people with disabilities. The Guidelines & Standards issued under the ADA and other laws establish design requirements for the construction and alteration of facilities. These standards apply to places of public accommodation, commercial facilities, and state and local government facilities.
If posted on an accessible website, tax forms need to be available to people with disabilities in an accessible format on the same terms that they are available to other members of the public – 24 hours a day, seven days a week, without cost, inconvenience, or delay. A staffed telephone line that sent copies of tax forms to callers through the mail would not provide equal access to people with disabilities because of the delay involved in mailing the forms.
The ADA has been criticized on the grounds that it decreases the employment rate for people with disabilities and raises the cost of doing business for employers, in large part due to the additional legal risks, which employers avoid by quietly avoiding hiring people with disabilities. Some researchers believe that the law has been ineffectual. Between 1991 (after the enactment of the ADA) and 1995, the employment rate of men with disabilities dropped by 7.8% regardless of age, educational level, or type of disability, with the most affected being young, less-educated and mentally disabled men. Despite the many criticisms, a causal link between the ADA and declining disabled employment over much of the 1990s has not been definitively identified.
Decided by the US Supreme Court in 2002, this case  held that even requests for accommodation that might seem reasonable on their face, e.g., a transfer to a different position, can be rendered unreasonable because it would require a violation of the company's seniority system. While the court held that, in general, a violation of a seniority system renders an otherwise reasonable accommodation unreasonable, a plaintiff can present evidence that, despite the seniority system, the accommodation is reasonable in the specific case at hand, e.g., the plaintiff could offer evidence that the seniority system is so often disregarded that another exception wouldn't make a difference.
Aloha Tatiana! I wish your questions had straightforward easy answers – and if you are government funded it kind of is. (See here: https://www.ada.gov/websites2_prnt.pdf) if you are not government funded, this is something that is currently being debated in the legal system. That being said, the WCAG 2.0 guidelines are a good set of guidelines to help protect yourself if you feel you should. (You can see more on WCAG here: https://www.yokoco.com/find-out-how-to-make-your-website-compliant/)