Pre-paid options
The most known mobile operators in the Netherlands are T-Mobile and Vodafone. The easiest way to get a pre-paid number is finding one store of those providers (tip: there are many of them in the most known Dutch cities). The SIM Card + activation + initial credit cost around €10 and €25.
Important: to have a contract plan you'll need a BSN (Citizen Service Number). So, until you get your BSN it's highly recommended to start with a pre-paid plan.
Activation
Each mobile operator has its specific activation process.
Vodafone requires you to call to a specific number, then you should wait until the end of the Dutch speech to get the English menu. After that you just need to follow the steps in this menu.
Airport
Almost all Dutch airports have their own public Wi-Fi network, in addition there are many other stores that "sells" Wi-Fi signal like Starbucks.