When you embark the ship you will be asked for a credit / debit card to be linked to the cabin for any expenses. You can use a debit card but NCL will apply to your bank for an authorised amount at that time. I am unsure of the amount, but they do warn you that the bank can hold this on file for upto 2 weeks after your cruise - If this figure was $100 per person per day on a 1 week cruise this could be as much as $1,400, so they do recommend that you use a credit card as this would not potentially effect the usual running of your bank account. You can however choose to pay by cash. In this instance at check-in you have to pay a deposit, then at regular intervals during your cruise you would have to go to reception to make any necessary additional payments - cash is not accepted anywhere on ship - except for the casino, everything is signed to your cabin. If going for the cash option this would also mean that on the last morning of your cruise you would have to go to reception to settle any debts - and there will be queues at this time.
You do have the choice to either prepay the service charge before you cruise at £5 per person per day (on the cruise invoice) or NCL will automaticaly add $10 per person per day onto your cabin bill. If you wish to pay tips to staff directly instead then you would have to go to reception and ask for this fee to be removed. - This is a form filling exercise which they try to discourage. However, there will still be a 15% gratuity added onto all drinks purchased in the bars / restaurants / mini bar etc.
Hope this helps.