1. Get one month visa at the airport.
2. The next day (this will take a while), go to your local wada (municipality) and get a document of your relation, son/daughter of the local person who owns a Nepali citizenship etc etc. I have no clue how long it will take but I have heard it will be a pain.
3. After you have the relation document, go to immigration office near Dillibazar. Take your foreign passport, recent picture and the relationship document. There is an office outside, pay them some money and they will take care of it, $3-$5.
4. Go to room 206 (3rd floor) and submit the document. Both party of the relationship should be there (son and dad both). They will ask few questions and once approved,you pay the fees (room 106 downstairs, 2nd floor). It is $5 for a months. You can get visa for a year at a single visit. Then they will tell you to leave your passport, the original relationship document and come back after few hour and half.
5. Eat some good food at Ananmnagar, chill out and then go pick up your passport. Done.