How can I properly ask a teller in a shop or mobile company office to top up my mobile phone?
As far as I understand, the proper word is "recargar" but I have no idea how to use it properly. (btw, I need this expression for the Mexican Spanish)
The word you are looking for is recargar.
This applies to teléfonos prepago (prepaid phones) that have to be recargados before you can make calls or use the internet.
This applies to most of hispanomerica, including Mexico, as you can see on Movistar's Mexican website, where you can recargar en línea (pre-pay online).
Even if you could go to a place to "top up" your prepaid phone, it is more and more common to recargar online.
To ask a clerk to "top up your phone" you would say:
¿Podría, por favor, recargar 20 pesos a este teléfono?
They will then ask for your phone number and the money.