Everybody is liable to pay tax. Which means that you have to make your tax return (inkomstenbelasting) if you work for yourself. If you are in employment, your employer pays taxes (loonbelasting) for you.
If you have just one job, your employer is responsible for your tax and social insurance payments (PAYE). If you have no further expenses such as mortgage or alimony, you do not have to make a tax return.
If you have several jobs, or are self-employed / working freelance, you should request and complete an Income Tax return. You also have to keep basic books: opening and closing balance sheets and a profit-and-loss account. But you can offset the costs incurred in carrying out the work against tax.
Turn over of VAT (btw)
People who just started their own business usually work as a freelancer. As a soon as you have an income, you have to apply at the Chamber of Commerce. The Tax Administration (Belastingdienst) decides if you are obliged to pay turnover tax. This depends on the amount of the expected turn over. There is special legislation on VAT for teachers.