How do you text an Irish mobile from a UK mobile?

If someone else is calling you, they should dial your number the same way they do when you are in Ireland. The mobile network will find you automatically.

If you are calling a number in England, or anywhere in the UK, the best way to dial it is using the full international number format. Replace the trunk prefix 0 of the UK number with country code +44 (including the plus sign).

If you are calling a number in Ireland, the best way is again to use the full international format. Replace the trunk prefix 0 of the Irish number with country code +353.

If you are calling a number in Italy, dial the country code +39 followed by the full Italian number. Do not drop the leading 0 of the Italian number. (Italy is an exception to the general rule.)

To call some other country, use the full international format, starting with the plus sign and country code, then the city code (usually, but not always, dropping the trunk prefix 0) and subscriber number.

(The plus sign means "insert your international access prefix here." From a GSM mobile phone, you can enter the number in full international format, starting with the plus sign. The most common prefix is 00, but North America (USA, Canada, etc.) uses 011, Japan uses 010, Australia uses 0011, and many other countries use different prefixes.)