Checking the status of your Pokemon with you is important in Pokemon Brilliant Diamond and Shining Pearl, especially if you want to evolve certain types of creatures in the world. Thankfully, you can do this with the Friendship Checker which can be found relatively early in the game.
As soon as you reach the Eternal City, you will find all kinds of shops and services at your disposal. However, to find the Friendship Checker Poketch app, you will need to go to the Pokémon Center in the city. In the main hall you will find a nice lady with long brown hair, a pink shirt and a green skirt. She is standing on the Pokéball emblem on the main floor. Go talk to her and she'll give you the Friendship Checker Pokétch app. It's easy to find her, and luckily, she won't ask you to run an errand in exchange for so much generosity.
To use the Friendship Checker app, press the right side button. Now, hover your mouse-like hand over the red button on the side of the gaming device. Keep pressing it until you see a screen with the Pokemon in your party walking around. Press A to see how they feel. If they are jumping, they are happy with you. There's a lot more to the friendship levels in Brilliant Diamond and Shining Pearl to understand, but this app gives you some basic feedback on how each of your party members feels about you.
While you are out and about in Eevopolis, you can go looking for a Ponyta. They are running in green patches of grass in this area of Sinnoh.