How do you extract the sending and receiving addresses, and the amount, from a Bitcoin transaction?
Bitcoin transactions are serialized into a hex string that contains all the necessary information to execute the transaction such as input and output values and origin and destination addresses. Blockchain.info decodes transaction hex strings to show this information.'

We can take the transaction you listed as an example and decode it:

Starting with the transaction hash:
2c1a83d5a511399f151571ff26925764ef73081251c239dd2eb6904304d7bcba

We get the hex string using blockchain.info's api:

https://blockchain.info/rawtx/2c1a83d5a511399f151571ff26925764ef73081251c239dd2eb6904304d7bcba?format=hex

Which gives us the hex:

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

Almost all bitcoin libraries (in whatever language) have functions to decode hex strings. Here's an online service that lets you decode the hex:

http://chainquery.com/bitcoin-api/decoderawtransaction

Pasting the hex from above will give you information about the transaction.