How to find out as soon as possible about a transaction to my payment address?
Most people look up the receiving address in blockchain.info , but the site is having some trouble lately. They show the transaction about a second after broadcast, and show how many confirmations a transaction has in the address page.

If it doesen't work, try another block explorer, some are listed below:

blockexplorer.com

blockr.io

blockcypher.com