We are not in the process of transitioning in this type of situation as we would see high productivity gains in every sector if we were. But for the sake of the argument, bellow is how I imagine such a future would look like. Note that basic income doesn't have to be part of it, but some form of redistribution will likely be necessary.

In a world where machines are better than humans at almost everything, unless we discover new laws of physics, machines will still require time and natural resources (space, energy and matter) to produce goods and services. Since there will no longer be a market for labor, the economy will be dominated by markets for readily available energy, space and matter (what economists sometimes call "land").

Robots will be in charge of automatically turning this energy and matter into the maximum amount of value for humans (hopefully).

For most people, "working" in this world will consist of going online, buying or trading an amount of energy, buying raw materials or spent matter that is ready to be recycled and pressing a "go" button.

Some people may also work on designing new better machines that produce finer goods. This will be mostly creative work as the technical part will mostly be automated.

People will not have to go out to work. Machine owners will be able to watch video of machines working maybe in an industrial park somewhere. The finished goods, spent matter (trash) and machines themselves, will be picked up and delivered by delivery robots.

If they wish for more variety, people will trade the production of different machines and they will trade different kinds of spent matter. They will also trade the machine designs and the land or space to host the machines.

The machines will sometimes have to be replaced when worn out or obsolete but that will also be done by machines.

The most important economic constraint will likely be global energy production likely based on what can reasonably be captured from the sun. People could own shares in energy production capacity.

Every day, as energy shareholders, people will receive their energy dividend, an amount of energy to be spent. They will be able to sell this energy, use it in machines to produce stuff or services or maybe store it in a battery.

There might be a level of inequality in this society. This will depend on how much governments allow ownership of things to be concentrated, especially ownership of energy production. Governments may redistribute so as to guarantee a minimal amount of livable space, energy and matter to everyone.

In this future universe, this minimal amount of redistribution of energy and matter (ie. trash) will give people a very high amount of value without them having to work at all (unless they want to as creative endeavors).

Not a bad existence in my opinion.

Something like giving people a minimal number of shares in the economy, shares of energy production or shares of GDP could make for an interesting way to implement something like universal income in a futuristic scenario.

It would probably create better incentives for people to want to grow total output or at least not hurt it too much than to tax and redistribute a fixed amount. It would also make the system robust to variations in real GDP due to natural causes, disasters etc. It's hard to fulfill a real basic income promise when total production suddenly drops.