Layer 2s (rollups) work by batching many transactions together to save computation and storage. The post the hash of the data so anyone can check that it is accurate and then record the change in state from start to finish on the main chain. This saves space and computations by the network

To use a layer 2 you need to bridge or use an exchange that lets you withdraw directly to a layer 2.

If your goal is to avoid fees (note that saying “miner fees” is unnecessary, you can just say fees. The miners aren’t charging the fee, the protocol and supply and demand determines that) then using an exchange that lets you withdraw directly to a Layer 2 is your best bet. Bridging can be expensive otherwise.