The above question is correct but it used the old library which not support any more. Current Mysten Lab have change to package @mysten/sui

First you need to get the key pair from mnemonic or private key

const exampleMnemonic = 'result crisp session latin ...';

const keyPair = Ed25519Keypair.deriveKeypair(exampleMnemonic);

https://sdk.mystenlabs.com/typescript/cryptography/keypairs#deriving-a-key-pair-from-a-mnemonic

Then use that keypair to create signature for transaction https://sdk.mystenlabs.com/typescript/transaction-building/basics#transactions

const result = await client.signAndExecuteTransaction({ signer: keypair, transaction: tx });
await client.waitForTransaction({ digest: result.digest });

You can read more at https://sdk.mystenlabs.com/typescript/transaction-building/basics#transactions