Instead of sending the transaction out on the p2p network for any miner to include, you just send it privately to the specific miner you want to mine it. Nobody else knows about it, so they can't include it in their blocks.

The problem (and the reason this really isn't a useful money-laundering method) is that people watch incoming transactions and blocks, and if a block is mined including a transaction that was not seen previously, it's a strong indication that there's collusion going on.