I am a legally blind 4E D&D player and DM. I have been playing for many, many a decade now. I have utilized several different approaches over the years.
If the blind person has access to speech synthesizer software on a laptop, mobile device or other electronic medium, there are all kinds of compatible applications available. Mach Dice on iPhone for one.
If all else fails, it is very easy to create an Excel spreadsheet to roll any number of dice and pressing F9 to refresh. The easiest formula to use is:
for a random roll between 1 and 20. Older versions of Excel don't have
RANDBETWEEN, but you can still use:
The screen reader can read the results aloud. If the roll is to be secret, just use headphones.
If you do have an accessible computer, logging in to accessible chat rooms with your DM allows for secret messaging back and forth for extra dramatic role-playing effects.
The cork board idea previously mentioned is BRILLIANT! For low vision users like me, using high contrast dry-erase grids is good. Laser light pointers can be useful, too. For temporary zones, pipe cleaners can be cut and bent into whatever shape the wall or zone takes. Wires also work. Having a major distinction between good guy tokens and bad guy tokens really helps the blind person keep the entire board in mind at once. Realize that even by touch, the blind person has to hold a lot of pieces of information in their brains all at once, so the more distinctively tactile the map features are, the easier it is for them to understand what’s going on, and to better strategize.
Putting character sheets in an accessible electronic format is also nice since Braille copies are not as easily updated during game play. Gold, hit points, treasure and (in 4E) powers are much easier and faster to keep track of when you have the Copy/Paste, and Find commands at your disposal.
The biggest stumbling block for me as a player (not DMing) is keeping up with battles when it isn’t my turn. Thus, I feel less engaged than I normally would if I could keep up. I am stoked about trying the cork board idea soon. Other tools I’ve thought about using are puff paint grids, Braille labeled monster tokens, metal-backed dry erase board with magnetic tokens, etc. As a DM, having a rules lawyer in the group is always useful when you quickly need to reference something technical! Braille labeling status effects or using large print status cards has proved handy when learning the game.