Are you in the U.S.?

I am on long-term SSI for a lifelong neurological problem. It took them . . . I think it was five months to approve my case. First I had a very long interview (almost exclusively about finances) at the Social Security Office. Later they got paperwork from my doctor, and then sent me to a doctor of their own to give me a perfunctory examination.

A friend was on (usually short-term?) SSDI for depression and alcoholism. I think it would have been hard to deny given his number of rehab stints and one lengthy hospitalization. I don't know as much about how his process went or how long it took to approve (and he's dead now, so I can't ask). If you have a decent work history you'll probably be going through SSDI.

A lot of sites will tell you to contract a lawyer, but although they say they're free they might take a percentage of whatever tiny amount you end up getting, so if you have the medical documentation I would save the lawyer for if you need to appeal.