Yes, you can buy a local sim card in Nepal which comes in dominations of NPR 500, 1000, 2000 etc which is the equivalent of US$10, 20, and 40. There are instructions in English on how to activate the card which requires several steps like calling an 1800 number, entering the card number and then the code (which is under a silver overlay that you need to scrape off to reveal the number) If it is too much trouble, the vendors will willingly do it for you for a nominal charge of only NPR 10 (about 20 US cents). Sometimes this charge is already added to your purchase price for the vendor to earn a small commission which also entitles you for the activation service.
These cards can be bought from any cellphone shop or bookshop/merchandise stores that displays the "Mobile" sign over it's doorway.
There are two sim cards available in Nepal, namely Mero, and Namaste. Both are identical and you can choose from either. More information here:
I have used both and the service is good and instant although some natives insist that Namaste has better reception than Mero in terms of voice conversation.
Oh yes, whereas Mero can only receive and make calls in major cities in Nepal, Namaste can cover the whole country even in the suburbs. So take your pick. about 8 years ago