Most banks have a variety of account types. The easiest accounts to open is a savings account (Spaarrekening) or current (checking) account (Betaalrekening). They both usually give you a debit card to withdraw money from ATMs and pay in shops and restaurants.
Payment methods in the Netherlands
Most bills are paid by money transfers from one bank account to the other. This can be done by telephone or the internet. Paying bills through the Internet is very popular in the Netherlands.
There is an option to pay bills automatically by means of an acceptgirokaart (direct debit instruction), often shortened to acceptgiro. You fill in a payment slip with the amount, your name, account number, the payee's name and account number. You then drop it in the mailbox at the bank, or put it in a freepost envelope provided by your bank and drop it in a normal mailbox. This is a very common way of paying in the Netherlands.
Automatic direct debits are also very common and may be required for certain services (e.g. mobile phone contracts). You need to fill out a machtigingskaart, which is a bank instruction where you state that company X can take money out of your account every month.
All banks offer credit cards
To be eligible, you need sufficient income. You will also pay a yearly fee, and maybe an additional monthly fee as well. Credit cards are not widely used/accepted in the Netherlands. The Dutch tend to use them for larger purchases such as renting a car, buying over the internet or when travelling abroad.
Cash machines (ATMs)
Whichever bank you choose, make sure they give you a card that you can use internationally. The Netherlands is relatively small and it is probable you may travel to at least one neighbouring country while you are there. Most cards are international anyway, however, you should double check. Look for the Maestro and Cirrus logos as these networks allow you to withdraw money in most countries internationally. Withdrawing money in other EU countries is free of charge. In non-EU countries, you may be charged €2 or more per withdrawal.
ATMs are called geldautomaten or pinautomaten in Dutch. Every reasonable sized town in the Netherlands has a few and larger cities have many. You can use any bank's card in almost all other bank's ATMs in the Netherlands (check with your bank for possible charges). So if you have an ABN-AMRO card, you can also use it in the ING pinautomaat at no extra charge. This is called gastgebruik (guest use), but you can only do this once every 24 hours.
What is a Chipper?
Old Dutch debit cards have a chip on them which the Dutch call the Chipknip or Chipper. However, the chipknip is no longer being accepted as a valid payment method as of 2015.
Most banks open 09:00-18:00 Monday to Friday. Some banks open late on Mondays at 10:00 or 13:00. On Saturdays most banks open from 10:00-13:00 or 14:00.