Some ladies have done this enough to have clear fees, guidelines and boundaries for the engagement. If she doesn't, then everything is up for negotiation and you should take the time to set clear fees, guidelines and boundaries. Fee-wise, you should expect to pay a flat fee (likely in the thousands) plus all travel expenses (flight, hotel, meals, etc.). If you don't know each other well, then the lady may want to set clear expectations on the quantity of sex (there are awful stories out there of guys basically locking girls in the room for non-stop sex fests). You should also allow each a reasonable amount of alone/private time.  

While on the trip you should conduct yourself in the same manner as if taking any romantic partner on a lovely vacation.  

Personally, I wouldn't take a trip with someone I haven't spent a substantial amount of time with - it'll be fun at first, but if you don't totally click, then after a day or two you may find yourself bored or annoyed with each other (try an overnight first).

Make it clear up front what's expected.  If on a cruise:
1) Do you meet at the port, who pays for her parking; or carpool, who parks where
2) Separate bed/bedroom?  Time apart is awfully nice if you sleep differently
3) During the days aboard do you take meals together, but do activities apart?
4) Playtime is expected when: once per day, twice, rabbits in a room?  Morning, evening, nooner, constant?
5) Shipboard expenses: what gets billed to the room, who pays?  Can she get a $30k diamond necklace?  What about a pool drink?  When are those reconciled?
6) Ports of call: what tours, who pays, do you have separate sightseeing desires?
7) What's the "out" if it turns out you piss each other off and need space?  Who pays for that space?
8) Trip insurance

I've done multiple nights & days on land so this was a lot easier.  We worked out a flat rate for her time based on what else I would be covering (room, meals, etc).  With disparate sleep patterns and styles, I've learned to get an extra bedroom yet still meet back together in the morning.  Can't stress enough how important quality rest is when you're together for extended periods.