Before you start

A valid passport or EU/EEA ID card (shown for prepaid; sometimes for contracts)
An unlocked phone, or buy a handset locally (eSIM widely supported if your phone has it)
For a monthly contract: a Dutch bank account with IBAN for direct debit (automatische incasso)
For most contracts: a BSN; phone-bundle contracts may trigger a BKR credit check

Step-by-step

1
Decide: prepaid for day one, or contract once you have a bank account
If you've just landed and have no Dutch IBAN yet, buy prepaid to get a working number immediately. If you're settled with a BSN and Dutch bank account, a SIM-only contract is cheaper for the same data. Pick a budget MVNO (Simyo on KPN's network, Lebara, Simpel, Ben) rather than a flagship store plan to save money.
In personWho: You10 minutes to decide
2
Buy a prepaid SIM with your passport (no registration)
Pick up a prepaid SIM at any KPN, Vodafone or Odido store, a supermarket like Albert Heijn or HEMA, or a kiosk at Schiphol. The Netherlands does not run a SIM-registration scheme, so there's no ID form to fill in; you may be asked to show a passport but nothing is filed. Insert it, top up online or with a voucher, and you're live in minutes. Lebara is convenient for newcomers as its site and packs are in English.
In personWho: YouSame day, ~15 minutesSIM ~€5-20; small data bundles from ~€5-10
3
Or sign a SIM-only contract online with a Dutch IBAN
Order a SIM-only plan from a provider's website (KPN, Vodafone, Odido, or a cheaper MVNO). You enter your details, usually your BSN, and a Dutch IBAN, then sign a SEPA direct-debit mandate so the monthly fee is auto-collected. Plans are often monthly-cancellable. A phone-plus-plan bundle typically adds a BKR credit check; a plain SIM-only plan usually does not.
OnlineWho: You (must already have a Dutch bank account)SIM arrives in 1-3 working daysSIM-only from ~€6/month (light data) up
4
Activate, set up the app, and confirm EU roaming
Activate the SIM or scan the eSIM QR code, then install the provider's app to track data and manage the plan. Every Dutch plan includes 'roam like home' across the EU/EEA, the UK and Switzerland, so your domestic allowance works on trips at no surcharge (subject to fair-use caps). eSIM is offered by all majors and by Simyo.
Mobile appWho: YouMinutes

Documents you’ll need

Passport or EU/EEA ID card
Dutch bank account number (IBAN) for a monthly contract's direct debit
BSN (citizen service number) for most SIM-only contracts
A top-up voucher or debit/credit card / iDEAL for prepaid credit

Things most newcomers don’t know

No SIM registration means prepaid is genuinely instant for newcomers.

Unlike most of the EU and many countries worldwide, the Netherlands has no SIM-registration law, so an arriving professional can buy and use a prepaid SIM with no paperwork, no proof of address, and no waiting period.

Source: DutchReview / Prepaid Data SIM Card Wiki

The real gatekeeper for a cheap monthly contract is a Dutch IBAN, not the SIM.

Almost all SIM-only contracts bill by automatische incasso (SEPA direct debit), which needs a Dutch bank account, and most also ask for a BSN. Without these you're pushed to prepaid until your bank account and registration come through.

Source: DutchReview

Skip the flagship stores: budget MVNOs run on the same networks for far less.

Simyo uses KPN's network, hollandsnieuwe uses Vodafone's, and Simpel/Ben/Lebara resell the big three. SIM-only from around €6/month or prepaid bundles from a couple of euros get you the same coverage without the premium price.

Source: Simyo / DutchReview

Your Dutch plan works across the EU at no extra cost.

EU 'roam like home' rules mean calls, texts and data on any Dutch plan (prepaid included) work at domestic rates throughout the EU/EEA, the UK and Switzerland, so frequent travellers don't need a separate roaming add-on.

Source: KPN / Vodafone / Odido roaming terms

Common mistakes to avoid

Assuming you need a bank account to get connected: you don't for prepaid; only monthly contracts require a Dutch IBAN.
Trying to sign a SIM-only contract before you have a BSN and Dutch bank account, then being rejected at the direct-debit/credit-check step.
Buying an expensive phone-plus-plan bundle (often a 12-24 month commitment with a credit check) when a cheap monthly-cancellable SIM-only plus a separate handset is more flexible.
Overpaying at a flagship store when a budget MVNO (Simyo, Lebara, Simpel, Ben) on the same network is much cheaper.