As an individual? I'd suggest researching the hardest problems for computer AI to solve, then picking a career in one of those areas. Generally any area to do with creativity and the human condition should remain viable for a long time.
Luckily, programming and design should remain relevant for quite a while.
I believe even customer service jobs are not immune to technological unemployment. I see no reason why a modernized automat couldn't replace most of the food service industry. And why couldn't an upgraded Siri replace most customer support workers?
The problem is when company owners replace human laborers with computerized laborers. CEOs are the ones who see the profits from the increased efficiency and the employees see nothing. This seems fine in a free market system yet if we follow through to the end game, we find incredibly efficient companies owned by a few people, with no human employees. If nobody is employed except CEOs, who will have money to buy their products? Robots can't buy stuff (yet)!
I believe the only solution is to pay people for robot labor. This may seem counter-intuitive, but when society has no income, there's nobody to buy the goods your robots have so diligently created.
Two solutions I've come up with are either a guaranteed minimum income or robot labor profit sharing.
An example of robot labor profit sharing is forming a union of "robot laborers" in which human employees invest in robots and receive the profits their robots generate. It would essentially be employees outsourcing their work to robots and receiving the profits.
One thing is certain. If we don't make significant progress on this solution, in favor of society as a whole, economic inequality will continue to increase until our economy breaks.
I am deeply interested in this topic and would love to hear from anyone who is working to find a solution to this problem.