It depends on the your company's insurance benefits. When I took STD, I had to fill out some forms, have my p-doc fill out some forms, fax it all in to the administration company (not my place of work, but the third party that administers the STD program) and get it approved. My p-doc has done enough of these forms for his patients that he knew all the right things to put down to get my leave approved. Then, I shot my manager an email and let her know that I was taking 2 weeks off for STD. She also received notice from the adminstrators that I was out on approved leave. Once that happened, my pay was managed through the STD program and I received full pay for the two weeks I was out. It was a pretty painless process, but I did have to start with my HR department to get going in the right direction.

Your best bet for figuring this out is going to be to talk to someone in HR. Ask about the company's Short Term Disability benefits and then if you do have that option, ask how to go about using it. Some companies don't offer it and some only offer it after you've been employed for a certain amount of time. You don't have to explain to anyone why you need to be out on leave, just that you need it.