How do I get an original degree from the JNTU Hyderabad online? How many days would it take?

  
You have to Fill the Applicaiton form for Original Degree Online.
Usually the Link for the application is 

http://epayments.jntuh.ac.in/onlineconvocationservices/

This Site may not work asusual Always. 

Pre - Requisites : 
1. Scanned Copies of A passport size photograph as prescribed in Site. 
   a color photo graph with white background, no shadow, no spectacles, 
   no hair falling covering face etc are some restrictions and size must 
   be around 6 to 20 kb( this may change). 
2. Scanned Copy of Consolidated marks Sheet(CMM). 
3. scanned Copy of Provisional Certificate(PC). 

while you fill the application form. 
1. you need the your current Residential Address, where you will receive the OD in Courier. 
2. Serial No. of the CMM and PC. 

You can do payments in two ways 
either you can pay using debit/ credit card. OR
you can download provided Bank Payment Challan form, fill in the challan and pay the prescribed amount (amount differs from candidate to candidate depending on some factors I dont know about the factors exactly) at your nearby SBH or SBI branches. 

after all this you get your OD to your given Address within a week to 2 weeks of time.