How will this system be funded?
Some will come from eliminating redundant social programs that overlap with providing a means by which everyone can live in dignity and participate in society, one of the goals of a UBI (universal basic income). Most will come from taxation that is progressive in nature. There are different taxes (flat, land, VAT, income, capital gains, financial transaction, etc.) that could do this, the specific one(s) used is still somewhat debated.
Won't too many people just get lazy?
You might think so at first, but there is some experimental evidence that this is not the case, that poverty is not a product of laziness as much as it is simply lack of control over any significant portion of society's resources, and that with some initial capital (reclaiming some of their society's resources), the previously-poor spontaneously become entrepreneurial.
And will menial jobs still get done?
Yes, only they'd have to be paid more, or made less menial (or less hazardous or morally objectionable) for similar pay. Essentially, the most marginalized would have more ability to reject the more exploitative labor conditions. It's not completely clear, but with increased labor costs there may be an increased incentive for companies to automate these positions, which isn't a catastrophic problem for the displaced worker, who has a UBI to fall back on, or perhaps use towards education or other ways of transitioning to a new career, however they choose to.
How is this system different or better than the system we already have in the Netherlands? The government provides you welfare (that actually is enough to live by as far as I know), the only requirement being that you apply for a certain amount of jobs every month.
One of the big things it does differently is be universal in nature. This cuts down on welfare bureaucracy, simplifying the system. How? Instead of a government body having to make sure that recipients are really poor, are really looking for jobs, etc. (which I'll get into more below), everyone gets a basic floor of income to build off of.
Treating everyone similarly in this way can allow very low administrative costs, because collecting taxes and redistributing income is something the government can do very well (here in the US, our Social Security program uses only 1% of its budget for administrative costs).
On the other hand, doing what we do now naturally leads to a "policing" of recipients' behaviors. Depending on the system (I'm not as familiar with Netherlands' in particular as I am with the US and UK) recipients may have to do things like: constantly prove that they are who they say they are, prove that they're poor enough to receive assistance, prove that they're looking for work with the regularity or in the way the unemployment office wants them to, prove that they're attending the retraining or professional development programs the social assistance office wants them to (even if they don't think those programs' are useful to their personal situation), etc. ad nauseum.
Collecting the correct identification information, filling out the required legal documentation, making trips back and forth to the social assistance offices, etc. is time-wasting and inefficient for everyone.
Constantly looking over the shoulders of those in need of assistance also strips them of agency over their own lives. If you want a person to develop self-direction in their own lives you can't constantly police their every move and then expect them to act freely or creatively or entrepreneurially, or like they aren't being controlled (because, in the worst welfare systems, they are), like if they take one step out of line they won't get to eat.
On top of that, many times there will be a patchwork of social assistance programs that try to cover all the needs of a poor person (when you don't trust them to make purchasing decisions for themselves and their own good, but instead try to create multiple government programs to do it for them in the form of in-kind, rather than direct cash transfer welfare), but end up missing some of their needs, or over-covering them redundantly. They may treat people with similar needs differently, or different people too similarly, creating unfairness and unsatisfactory outcomes.
Predicting what goods are most efficient for you to consume, and what work is going to be useful in the future that capitalizes on your own personal strengths is a complex task, that requires individual direction. I think government is well suited for some tasks, but not always for these two, and that people are better left to their own devices to determine things like how their own best way to "work" (or contribute to society) is.