In terminal:
anvil
Note: You can check in the anvil terminal if the deployment process worked. Every interaction with the chain is logged in the console.
forge script script/DataMapping.s.sol:DataMappingScript --fork-url http://localhost:8545 --private-key 0xac0974bec39a17e36ba4a6b4d238ff944bacb478cbed5efcae784d7bf4f2ff80 --broadcast
Note: Here is the guide of how to deploy scripts via forge.