Generally the calculations tend to be based on an increased tax on consumption (people who are better off spend more money, so they end up paying more into the system) and/or the reduction of expenses in a lot of the social welfare system (which can largely be rolled into the basic income).
Some designs assert that the basic income should simply be paid to every citizen regardless of other sources of income. Other models propose a model with a soft cut-off point (so for every dollar beyond a certain baseline of income you get some fraction of a dollar less basic income, up to a level where you -- again depending on the model -- either start paying it back or simply don't get any basic income at all). In any case the idea is that (unlike with welfare models like the one we have in Germany[0]) for every dollar you earn you actually end up with extra cash in your pocket.
Ideally the basic income should be high enough to provide a frugal but sustainable standard of living with access to everything necessary to participate in the market. But arguments can be made for lower amounts as well.
[0]: One problem with the German welfare system (and similar ones) is that if you receive welfare benefits and earn money, that money is subtracted from the benefits you receive at a rate of pretty much one-to-one. So if you (hypothetically) get 400 euros in benefits and then find a job that pays you less than 400 euros, you effectively end up with the same money you'd have without the job. This creates an unintentional incentive for welfare recipients not to take on low-paying jobs (frequently the only ones they qualify for) which is then clumsily counteracted with various legal constructs (like forcing people to take job interviews or accept job offers for jobs they are not a good fit for at all). It's not a terrible system, but the design flaws are obvious.