[DiverDude]

The most time-efficient, cost-effective, and pleasant way to do this is to do all the classroom work and pool dives here, before you go. The course costs less here and you don't burn vacation days sitting in a classroom.

Then, if you can, try to pick a resort with a dive operation on the premises. This will make is a LOT easier and you will spend less time away from the family. Finally, pre-arrange with the dive shop to do your open-water "referral" dives with them. You will just pay for 2 dives (there will likely be a surcharge because you will need 1-on-1 time with a divemaster on those dives -but it's not a lot).

When you arrive, they will take you on an easy dive or perhaps just into the surf and have you go through some basic exercises. You'll then do a couple of easy and fairly shallow dives (50' or less) and as long as you can recover your regulator, maintain buoyancy, clear your mask underwater, etc. you're done and they will certify you. You will then receive a temporary C-card. A permanent one will come by mail later.

That's it. You can now get cylinders filled and dive where you want (subject to your experience level and the judgement of a divemaster).

Enjoy.