You can look up cryptocurrency transactions by using a Blockchain Explorer.
A Blockchain Explorer is a tool for viewing and querying blocks on the blockchain. It works like a web browser (e.g. Firefox or Google Chrome) but is connected to the blockchain rather than the internet.
The main function of a cryptocurrency block explorer is to enable anyone with a connection to the internet to track all transactions taking place on the blockchain in real time.
See also: Blockchain, Altcoin, Wallet.