If we are in the same place, either someone else will roll for him or he'll roll and we'll tell him what he got (and he has little choice but to trust us :)). If we aren't in the same place, he rolls virtually (did you know you can type '/roll 1d20' in Google Hangouts and it rolls?) and gets the result via a screen reader.
For a while he was DMing and he would use a screenreader to access his notes plus the rolls. We don't typically use maps or boards, but instead try to do it all with descriptions of places. It does mean that the rooms we enter all tend to be fairly simply shaped, and it's possible that each of us has pictured a slightly different room, but it all works out in the end.
I love theater of the mind sessions. Maps have their purpose, but it's so much more fluid and imagination-intensive when your boundaries are visualized by your mind. The game loses something when you tie it down with predrawn environments and grids.
For a while he was DMing and he would use a screenreader to access his notes plus the rolls. We don't typically use maps or boards, but instead try to do it all with descriptions of places. It does mean that the rooms we enter all tend to be fairly simply shaped, and it's possible that each of us has pictured a slightly different room, but it all works out in the end.