As you want to appear in UPSC Engineering Services exam and asking for process for Online Application, so I am telling same for you

Before applying online candidates have to scan the copies of photograph & signature.

Go to the UPSC official website
Click on “Online Application for Various Examinations of UPSC”.
Click on “Part – I/ Part – II Registration”.
Read the Important Instructions & fill the form with all the relevant details & submit the application form.
After successful registration, a unique registration ID will be allotted, note down the ID & password.
Now fill the personal profile, contact details, age relaxation if applicable.
Now fill the details of qualification, experience.
Now fill the details of Professional Registration, Language, Miscellaneous Module.
Now Applicanthave to choose the Recruitment Test Centre.
Now candidates have to upload documents in Document Upload Module
After uploading photograph & signature preview the ORA form and check the details carefully.
Now click on the submit button
Candidates can Pay Online using the Internet banking facility in SBI or other associated banks or can pay through Visa/ Master Debit or Credit card issued by any Bank/ Institution.
Here the Transaction ID & Date of Registration details will directly uploaded automatically.
Now pay the fee through cash at any branch of State Bank of India through the Pay-in-Slip
A transaction ID will be given, again revisit the website and click on the “Click here to view your Previous/ Currently active applications”.
Log in by registration ID & password, candidates can see “My Active Application (My draft Application)” link.
Now fill the details of transaction ID and Date of Transaction if paid through cash.
Click “Continue”, check the details of fee and submit the application.
Now take the printout copies of application attach the attested copies of all documents and keep it for future use.