Phone and internet connectivity is very easy in Nepal.
You will find that nearly all hotels and tourist café’s in Kathmandu and the main tourist towns will have free wifi available to guests. In the trekking areas lodges even in fairly remote areas will have wifi available (at additional cost). In fact there is a wifi hotspot at both Everest Base Camp and Annapurna Base Camp. However these mountain wifi hotspots can be affected by adverse weather (such as heavy snowfall) and may not be available all of the time.
On arrival in Nepal you can purchase an N Cell sim card, all you need is a passport for identification. You can buy reasonably priced data packs and call credits. This will ensure that you are able to make local calls to stay in touch with your tour operator in case of emergency and access mobile data when not in any wifi zones. In the more remote trekking areas you will not be able to access mobile data but will have access to wifi in many of the lodges where you will be staying.
If you need extra calls or data during your trip you can easily buy top up credit at most grocery stores even in remote areas and dial the credit onto a data pack for your phone.
If you are not a techy person than you will find that nearly any Nepali person will be able to assist you in adding the credit or data service to your phone.