With casual usage, it is not very anonymous at all. Transactions occur between cryptographic addresses, and anyone can create any number of these addresses. However, bitcoin can be traced back to your IP address.  

A company like Chainalysis have been identifying wallets that are linked to criminal activity, such as darknet transactions

To look up a Bitcoin transaction, users can visit: https://www.blockchain.com/explorer and use the search bar to learn more about a particular Bitcoin address. However, here is what actually happens behind the scenes of a BTC transaction, https://www.altcoinsidekick.com/bitcoin-basic-blog/behind-the-scenes-of-a-bitcoin-transaction.