Using your iPhone abroad is expensive, so to keep costs down make sure you have Data Roaming turned off:

Settings -> General -> Network -> Data Roaming

Furthermore, make sure that auto-checking of email is disabled:

Settings -> Mail -> Auto-Check

Finally, turn off visual voicemail before you travel:

Dial 1760 to switch the divert to voicemail off and dial 1750 to switch on the divert to voicemail.

Travelling abroad with iPhone: usage and costs