I have been asked to implement cryptographic operations using elliptic curves. I would like to get precise algorithms for various processes like key generation, digital signature and verification. I found this link, but I just want confirmation on the algorithms provided there are correct or not. I would also like to know if there is any standard site for this topic whose information are authentic and can be trusted.
Standards for Efficient Cryptography Group has published SEC1: Elliptic Curve Cryptography (pdf) about elliptic curve algorithms. If it does not explain the mathematics well enough for your purposes, there is also Fundamental Elliptic Curve Cryptography Algorithms (RFC 6090, from IETF) you could look at.
There are a lot of issues you can run into, so hopefully this is an exercise of some kind, rather than someone expecting you to write production code from scratch. For production code I would recommend using existing libraries.