But why will people work if they don't have to?

People will have to work, but it will be voluntary. If people didn't work society would obviously fall apart. To establish socialism the vast majority must consciously decide that they want socialism and that they are prepared to work in socialist society.

• Work is part of human life. Today rich people work when they don't have to, because they, like many of the rest of us, enjoy working. Many people work harder at their hobbies than they do at work. It is the nature of employment that makes it "work" instead of pleasure. Work needn't be a part of the day that we wish would end.
• People enjoy creating useful things. Instead of producing junk that people only buy because they can't afford quality, every worker will be able to produce quality products for themselves and others, and know that other workers will be doing the same.
• The workday will be shortened. Many jobs (such as those dealing with money, or war, or poverty) will not be required at all. The people doing those jobs now, will perform work that actually produces goods and services that people want.
• People will gain respect for doing jobs that others might find unpleasant, or the unpleasant jobs might be shared around. Many of the unpleasant jobs could be made more pleasant and some could be done away with.