The Dutch tax office is pretty decent, although slightly overburdened. Don't expect a lot of help, but they're not generally known for making a lot of problems. Digital copies are fine, for instance. They will send you your first VAT notice.
You probably would have known if your company would have been incorporated, so I'll assume you're just trading as a natural person. That means you still have to file VAT returns, but the business income is just filed annually as "other income".
For the VAT part, you'll need to invoice your customers. Keep a copy of those invoices for your own bookkeeping, and keep track of the matching customer payments. Together these form the chief evidence of your VAT obligation. You also have a VAT deduction from your purchases (it's a Value-Added Tax, after all). Again, keep receipts. The usual VAT period is 3 months, so you'd pay VAT 4 times a year. But if you would pay less than 1883 euro, you might not need to pay at all and just need to file annually
The income part is easy with the receipts you had for VAT purposes anyway.
Dutch Tax Office, VAT, in English