You would need to check with your provider if your cell phone is working in Nepal. However it is quite easy to buy a Nepali prepaid SIM card through Ncell. All you need is to show your passport and have passport picture. Certain areas in the mountains might not have constant reception. In all touristic areas (hotels and restaurants) you will access to free WIFI. You can also buy an internet package through Ncell if you already have the prepaid card. During trekking some guesthouses and lodges have wifi however you will be charged for this service.
