All your shipboard charges, except for the casino,will be put on your account, including the tips (if you choose).
You'll need cash for in port purchases for smaller items you wouldn't normally use a credit card for, tips for excursions guides, lunches etc. PLUS if you like to gamble in the casino on the ship, or play bingo.
I think a "safe" # for amount of cash to bring along is $100/person/day.
On most cruise lines your tips are put on your shipboard account, which is credited to your credit card. You are basically paying for everything with your credit card.
You may give additional money, in cash, if you feel an individual went above and beyond in service. This is by no means required.
The amount of cash to bring is widely open to what sort of spending you plan on doing. I personally take about $100 in small bills for per-cruise tips and cab fare to and from the ship and then budget the $100 pp/day. That includes onshore cash purchases, taxis, wife's gambling and other incidentals.
Other people will be very comfortable boarding with $200 in cash and then use their credit card for all other purchases. It is up to you. You can obtain cash on your shipboard account from the casino or at the Pursers Desk. You can take travelers checks, etc.
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"There is a great difference between being well traveled and just having been to many places." ~Me
What ship are you cruising on. Some will automatically add the tips to your shipboard account, which will get charged to your credit card on the last day of the cruise, some still do it the old fashioned way with cash in envelopes. Even those cruiselines will give you the option to put the tips on your account if you want to. I find this much easier than bringing all that cash for tips, but thats also a nice way to do it, more personal.