I worked for the Greater Detroit Society for the Blind for three years running a BBS tailored for blind access and worked with a number of blind users on how to better meet their needs, and with newly blind users to get them acclimated to the available hardware and software offerings that were available at the time. If nothing else, I at least learned to read Braille as a hedge against the case where I ever wound up in the same situation!
The majority of blind computer users and programmers use a screen reader of some sort. Jaws in particular is popular. Fortunately, most major applications these days offer some form of handicapped access. You may have to tune your environment slightly to cut down on the chatter, e.g. consider disabling Intellisense in Visual Studio.
A Braille display is less common and is comparatively much more expensive and can show 40 or 80 columns of text, and can be used when exact positioning/punctuation is important. While a screen reader can be configured to rattle off punctuation, a lot of people find it distracting, and it is easier in many cases to feel your way through it. Jaws can be configured to drive the display, so you're not juggling accessibility applications.
Also, a lot of legally blind users still have some modicum of sight left to them. Using high contrast backgrounds and the magnification functionality can help a lot of these users.
Using ToggleKeys in Windows will let you hear when you accidentally tap one of the modal 'caps lock', 'num lock', 'scroll lock', etc. keys as well.
I know at least one Haskell programmer who uses a screen reader and who explicitly programs without using Haskell's layout rules, and instead opts to use the rather non-idiomatic, but supported {;}
's instead, because it is easier/less distracting for him to get his screen reader to read off punctuation than for him to figure out exact indentation that complies with Haskell's layout rules. On that same note, I've heard some grumbling from a couple of blind programmers about when they have to write Python.
Ultimately, you learn to play on your strengths.