There are currently two methods to connect to the Palm network:

Infura is an infrastructure node service that runs nodes on the Palm network and exposes their RPC API endpoints over HTTPS. Although the Palm network is a separate network from Ethereum, your Infura account and project information is used to authenticate you on the Palm network.

Detailed instructions for connecting to Palm network with your Infura account can be found here:

• Testnet - connect to Palm network’s testing environment. This is useful as a staging environment and for long-term testing. You can use the Palm Network Bridge to transfer assets between Palm Testnet and the Ethereum Goerli testnet.
• Mainnet - connect to Palm network’s production environment. Contracts and accounts in this network hold real value. You can use the Palm Network Bridge to transfer assets between Palm Mainnet and Ethereum Mainnet.

Alternatively you can use Blast's RPC API to connect to Palm Testnet or Mainnet networks

If you prefer operating with your own local EVM instance there are instructions on how to install, setup and run a transaction node on Run a Transaction Node.