// Subscribe to an event
empApi.subscribe(channel, replayId, $A.getCallback(eventReceived => {
    // Process event (this is called each time we receive an event)
    console.log('Received event ', JSON.stringify(eventReceived));
}))
.then(subscription => {
    ...
});

{
  "data": {
    "schema": "xxxx",
    "payload": {
      "My_Custom_Field1__c": "value",
      "My_Custom_Field2__c": "value",
      "CreatedById": "xxx",
      "CreatedDate": "xxx"
    },
    "event": {
      "replayId": 11
    }
  },
  "channel": "/event/My_Event__e"
}

empApi.subscribe(channel, replayId, $A.getCallback(eventReceived => {
    // Process event (this is called each time we receive an event)
    console.log('Received event ', JSON.stringify(eventReceived));

    // parse the JSON
    var jsonRes = JSON.parse(JSON.stringify(eventReceived));

    // retrieve the custom field values now
    var myCustomField1 = jsonRes.data.payload.My_Custom_Field1__c;
}))
.then(subscription => {
    ...
});