I am new to Bitcoin. How can I integrate Bitcoin payments into my website which is designed using ASP.Net?
Here is a book which teach you some basics of bitcoin programming https://programmingblockchain.gitbooks.io/programmingblockchain/content/
There is a comprehensive Bitcoin library for .NET called NBitcoin. You might want to check that out.
For the sake of simplicity, you can consider third party options such as Blockchain.info or Blockcypher.com. They provide API for developers to talk to blockchain in a simple way. They don't have official libraries for .Net, but you can use plain HTTP/HTTPS request to communicate with their servers for REST traffic.
From ASP.Net, you could use NBitcoin for tasks such as building and signing transactions, calculating wallet address, etc...
And to accept payment in coins, take a look at the HD Wallets from those providers. In summary, you can generate a unique address to each transaction and customer. When they deposit coin into that address, you can constantly check the API or register callbacks for alerts and confirmations.