Being a US citizen does not speed up US visitor visa process in India nor it is a guarantee of sponsered person getting visa.
The case will be decided by consulate after looking at it through consulate’s eyes.
In brief. parents DS 160 forms are to be filled. Then profile has to be created and later payment of consulate fees has to be made.
Later Appointments have to be taken.
First day will be for fingerprinting at OFC and second day will be actual Interview at Consulate where they have to go with supporting documents like yr sponsorship letter , copy of yr passport etc.
Fingerprinting and consulate Appointments can be on consecutive days or with a gap of maximum 14 days.Reasonable time between start of application process to Consulate Appointment is between 2 to 4 weeks depending on speed and accuracy of the person concerned
Detailed visitor visa process in India for USA would be a long article. Above is the procedure in brief.
Most of other sites give a mixture of some correct and some outdated information. As layman you do not know which information is correct and which is outdated
This is the only site does not give outdated information