You incentivise productivity the same way you always have, by paying for it. The UBI just moves the incentive from "I have to do this or I'll die" to "I can do this and make a better life for myself and my family".
I'm generally a pretty conservative/libertarian sort of person, and as such UBI makes me more than a little uncomfortable, but I definitely think it's worth thinking about, and disussing amongst people who won't react to it based on knee-jerk predispositions. And at some point, I think it may well become preferable to the alternatives. What kind of changes (both positive and negative) would we see if we used a UBI to completely replace welfare, SNAP, social security, unemployment insurance, disability insurance, and the minimum wage? It's hard to know, but from a basic trade-off standpoint, would the amount of people who decide that living on a UBI is enough for them and permanently slack off balance the amount of people who are afraid that if they get a job, their government checks will stop (whether or not that's a valid fear)? Would the economy find a new equilibrium where every job that Mike Rowe has showcased would suddenly become significantly higher-paying (and much more effort would go into automation for those jobs) because no one *wants* to do them, and people pre-UBI are only willing to if they have no other choices but starvation?
And how would people abuse this system? If everyone has a guaranteed income for life, will people take advantage of the UBI-only "poor" by giving them loans that eat up their entire UBI and leave them just as broke as before? (The answer to that is yes, they will, so the real question is more like "so how do we prevent that from happening?")
In the US, I've heard a lot of people talk about our "Puritan work ethic" that says that work is its own reward. I think a UBI would really put that to the test. If it's true (and I personally believe it is) then people will work, even for next to nothing, with a UBI to keep them afloat. Maybe we even get rid of some of the laws that were enacted to keep workers safe from abuse by their employers, because those laws presuppose that you *have* to work to survive and so if an employer is abusive you don't have the freedom to say "screw you, I quit." (Or the laws are based on the notion that work is a finite resource, so if I'm working 80 hours a week, I'm taking food out of the mouths of someone who *could* be working half of those hours)
All in all, I think it's a fascinating subject, and one that deserves a ton of thought. Unfortunately, it touches so many nerves and goes against so many deeply held beliefs that it's hard to have a conversation about it that doesn't quickly devolve into an ugly mess (see also: this whole slashdot post) And that's a shame.