Being myself insured in the Netherlands, I am not 100% sure how it works for non-residents but the way health care is structured here is that there is no national health service but many independent providers and several private insurers. However, prices and insurance coverage are regulated.
In practice, general practitioner (huisarts) consultations are free at the point of use (billed directly to the insurer) but prescriptions and many other things are paid by the patient, at least in part. As far as I know, you should always try to consult a GP first and he or she will refer you to a specialist or hospital if needed.
Regarding the way you should use the EHIC, the best thing is to check the official app (iOS or Android) and always show the card whenever you seek health care. Apparently, one insurer, Agis, is responsible for claims for all foreigners using the EHIC (the English-language version of the website is apparently unavailable but there is a link to a PDF brochure in English at the bottom of the page).
In a nutshell, the EHIC provides you with a coverage equivalent to the “basic insurance” defined in the law so that a GP consultation should be free and other health care providers should be able to claim insured costs directly from Agis, which would basically acts as your insurer in the Netherlands.
If for some reasons some health care provider cannot take care of it directly, you might need to pay everything first and lodge a claim with Agis at the following address to get (part of) the money back:
Groep Buitenlands Recht
You will need to fill in the form provided on the website and send a copy of the bill, a copy of your EHIC and the IBAN number from your bank account. They also have a specific email and telephone number for international matters, they might be able to provide more details on what you should expect to pay should you need to be hospitalized:
+31 33 445 68 70
Finally, if everything else fails, you can still try to contact your insurance or health care administration in your country of residence. You should expect some paperwork and delays but they might still be able to reimburse some things. Waiting to be back and seeking reimbursement is not how the system is supposed to work so there might be difficulties but it's not completely impossible either.
Given that Dutch patients have deductibles (eigen risico) and a personal contribution to some expenses, you might have to cover part of the costs in any case. The EU app also suggests that some costs not covered in the Netherlands might still be claimed in your home country (specifically dental care if you are covered for it).