The Apply For Social Security Benefits page of the Social Security website provides information and links to apply for retirement, spouse's, Medicare or disability benefits online. It is not possible to apply for Supplemental Security Income, report a death or apply for survivor's benefits online.
Each type of benefit has its own application page. Each application page lists requirements to qualify for the benefit, information and documents needed to apply, and ways to check the status of a filed application.
If an application for disability benefits is rejected for medical reasons, it is possible to file an appeal online. The Apply For Social Security Benefits page contains a link to the appeal application.