The majority of phones these days have the capacity to send and receive calls and texts in the majority of countries. To guarantee that your phone does work abroad, check that it has the cellular technology GSM and quad band.
A key necessity to being able to use your phone abroad with one of the countries own SIM cards is to make sure that your phone is unlocked. A lot of phones are locked onto one specific network such as EE (orange/t-mobile uk networks) and will therefore only be compatible with those types of SIM cards.
If you phone is locked it is relatively easy to get in unlocked by either going to an independent store that offers phone unlocking services. Alternatively you can try and unlock it yourself by obtaining the unlocking code. I have never don this but a quick search on Google may bring up answers you need.
Once unlocked all you will need to do is buy a local SIM card in whatever county you are in.
If you are unable to unlock your phone for some strange reason then I highly recommend sticking to using wifi only. These days there are lots of places such as hostels and restaurants that offer free wifi so it is very easy to stay connected even without the ability to phone or text people.