When you receive Heroes, Troops and Loot in the game, a notification will pop up - or if you are not in the game, when you login - detailing each item that you have received.
Please note - if you are in the middle of a battle or on the map, you will not see the pop-up until you come back to base.
In case you missed the pop-up notification before seeing the items that you have received, you can also check by:
Tapping Menu > Inventory
The same thing is applied to Heroes and Troops. You can check that the new Heroes have been added to your Roster by:
Tapping Menu > Heroes
You can check that the new Troops have been added to your Barracks by:
Tapping Barracks > Troops
You can also check your Recent Activity Log.
Tap your Menu Icon -> Options (gear icon) -> Support -> Recent Activity