How long after a person sends you Bitcoins does it show up on blockchain?
On the blockchain.info website? Or in the actual blockchain?
That's two completely separate questions, and you didn't clearly indicate what you are asking about.
"the blockchain" is a database that every full bitcoin node on the bitcoin network has a complete copy of. It is a complete history of every bitcoin transaction that has ever occured. It is not "owned by", or "operated by", or "controlled by" anyone. It is maintained in a completely decentralized manner by a set of rules called a "protocol" that has been implemented by any software that communicates on the bitcoin network. If a transaction is in "the blockchain", then it is "confirmed". When the transaction is first added to "the blockchain" it has one confirmation. As additional blocks are added to "the blockchain" after the transaction, each additional block is considered to be an additional confirmation. On average blocks of transactions are added to "the blockchain" approximately every 10 minutes. How long you have to wait for any particular transaction to be added depends on how quickly blocks of transactions are being added, and on specific parameters of the transaction that determine if there is a financial incentive for someone to add the transaction to a block for you.
"blockchain.info" is a website that is created, owned, controlled, and operated by an individual person. That person just happens to have named their website after a feature of the bitcoin protocol. They can do whatever they want with their website, and it won't have a direct effect on "the blockchain" or the rest of the bitcoin network. One of the features that the blockchain.info website offers is a list of transactions that their servers have seen occur on the bitcoin network. As such, if you have information about a transaction (such as the transaction ID or the bitcoin address), you can search for that transaction at the blockchain.info website and see if they are aware of it. If they are, and if you trust the operator of the blockchain.info website, then you can feel reasonably confident that the transaction exists on the bitcoin network. You can also see if blockchain.info website is aware of any confirmations on the transaction yet. Another feature that the blockchain.info website offers is a bitcoin wallet which allows you to send, and receive bitcoins at bitcoin addresses that you generate and they store for you.
