You can choose either a personal or an anonymous OV-chipkaart. Both cards cost € 7,50. You can buy an anonymous card at the 'Tickets & Service' desk at Leiden central train station or from an OV-chipkaart machine. For a personal OV-chipkaart, you will need to apply online or via regular post and submit a photo. Furthermore, you will need a Dutch bank account if you want a personal OV-chipkaart.
Your card can be charged at one of the OV-chipkaart machines strategically placed at train and metro stations. If you have a personal card, you can arrange for it to be charged automatically from your Dutch bank account.
You pay for your journey by swiping the card on entering and leaving the station or vehicle.
You can find all relevant information about the OV-chipkaart on this website.