How do I write a Apollo Server plugin to log the request and its duration

requestDidStart is called once per request and returns a map of request lifecycle hooks, so you can initialize any state persisted between the hooks there.

const LogPlugin = {
  requestDidStart(requestContext) {
    const start = Date.now()
    let op

    return {
      didResolveOperation (context) {
        op = context.operationName
      },
      willSendResponse (context) {
        const stop = Date.now()
        const elapsed = stop - start
        const size = JSON.stringify(context.response).length * 2
        console.log(
          `Operation ${op} completed in ${elapsed} ms and returned ${size} bytes`
        )
      }
    }
  },
}

Note that this will only work on a per-request basis. If you need something more granular, like tracking how long an individual field takes to resolve, you'd need to utilize a directive or middleware