There are public phones in Cuba, and they look like this

[![enter image description here][1]][1]

In order to call you need phone card (*tarjeta propia*) sold at [ETECSA stores](http://bestcubaguide.com/wp-content/uploads/2015/11/ETECSA-Facturas.jpg), it has blue color. Phone cards are sold in CUCs ($5, $10, and $20) and in Cuban national currency (3, 5, and 7 pesos).  
Addresses of ETECSA stores are listed [here.](http://www.etecsa.cu/contacto/red_comercial/)

Another, more expensive way, is making call from hotel landline, either from room or lobby.
But, all in all, I recommend you to apply some international roaming plan just in your homecountry and that's it. It would be much simpler and cheaper in majority of cases (it depends).
  [1]: https://i.sstatic.net/jh07Z.jpg