Obviously we've already seen the beginnings of this singularity, ATMs, self-checkout in stores, automation in production plants. But eventually I see automation as becoming total. Driverless cars have already been invented, they haven't been approved for sale to consumers yet but it's likely that's no more than 20 years away.
Robots are getting more and more agile, they will also get smarter. As they get cheaper to build they will begin replacing people in the work force, putting some people out of work but making products cheaper since the cost of labor would not be a factor.
This would cause growing pains in the move toward full automation of blue collar jobs. But as products get cheaper and some jobs for the moment remain non automated you might see job sharing. Prices being low enough for people to only need to work half the year to support themselves. The other half of the year can be worked by others temporarily taking care of the unemployment problem (this would happen naturally not by regulation).
But eventually automated robots would be agile, smart, and cheap enough that they could do any blue collar job. And even some white collar jobs. By that point people would already be able to buy their own robots for work around the house.
Soon after this point the same thing that happened in blue collar work would happen in white collar work. Automation would slowly take over. Eventually even things like brain surgery will be completely automated with no human input.
There would likely still be some jobs people would want to be done by human beings. Police for example, they would be augmented by robots for dangerous situations but humans would still dominate that profession as well as others like lawyers, judges and sports players.
By this time most of the population would be pretty much permanently unemployed since everything from mining materials for production to processing them, building the factories and making the products would be completely automated.
But if so few are employed who would buy the products? At this point since everything is automated the products themselves would be so cheap they would be practically free, unless the raw materials had to be purchased due to unavailability from mining. So how would such a society function?