In Kathmandu and Pokhara most hotels and guest houses offer free wi-fi.
Internet wi-fi access is widely available in most, but not all, tea-houses in the Khumbu Valley and Gokyo areas. The best current solution is to buy an Everest Link card, which will be valid in most tea-houses, for as long as you may be trekking. Be careful of buying a cheaper wi-fi card that is only valid in a particular village or lodge.
Wi-fi access is widely available on the Annapurna Circuit.
Internet access and phone connectivity is still poor on ‘off the beaten track’ treks in the Nepali Himalayas, don’t expect it.
Recharging batteries can seem expensive in trekking tea-houses, as sockets are not generally available in rooms. If it’s cold keep your battery next to you when you sleep.