There are multiple ways of staying in contact while in the middle of an ocean. Single Side Band radio (aka, SSB), satellite phone, message in a bottle... that might be it actually. The VHF radio you may have heard of can only transmit a few short miles.
We have chosen to go for a satellite phone. The Iridium Go! handset acts as a Wifi hotspot. With it we are able to make seemingly normal mobile phone calls, receive text messages and sorta kinda, look at the Internet.
The gadget costs around $1200 with the various bits and bobs you need to mount it securely out of the weather. On top of that there are monthly subscriber fees. $125 a month nets you a optimistically named Unlimited Plan. The 1980s era (I'm not kidding) download speed of the device means that at best, should you run it all month 24x7, you will have downloaded a few hundred megabytes. Not very Unlimited.
Thankfully the kind of data we need, weather and email, are usually small. Just about small enough.
We do have a SSB on board. To be honest, we've ended up using the Iridium go to organise SSB calls... and then fallen back to just calling with the Iridium because for one reason or another the SSB wasn't working... or wasn't working well enough to have a conversation. This could easily be ignorance of how to use the SSB on my part, but... the Iridium really is very good for basic communication.