The Expensive way is with a KVH receiver and pay by the character.
The cheaper way is with a Globalstar phone
and a data connection kit.
The SSB/Pactor/Sailmail way continues to exist as well...but if you don't have the SSB
or the Pactor
...it's kind of expensive too! Sailmail is $250 bucks a year for the e-mail service
Nothing REALLY inexpensive and reliable exists...but a lot of harbors do have wifi
hot spots that are open.
P.S. I should mention Iridium
as well as Globalstar
but for your trip, Globalstar has decent coverage and WAY lower per minute charges. Crossing an Ocean...Iridium is probably the best choice.