How do CNNs use a model and find the object(s) desired?
Though there can be a very detailed explanation for this question but I will try to make you understand much minimal words.

1) Cropping the images to a particular size isn't a necessary condition and neither is scaling. But put this way, it doesn't matter whether a dog is represented in a B&amp;W image or  RGB image because a convolution network learns features in the images which are independent of colors. Scaling and resizing help to limit the value of pixels between 0 and 1.

2) Once you have trained your CNN model, it has learned all the features like edges,etc. to recognize a dog in the image. Because the model has learned the features, it acquires certain properties like translation invariance which means that no matter where you position a dog in the image, it's still a dog and have the same features. How the model recognize it? It checks for the features of a dog, learned during training, no matter what the size of the new image is or where the dog is in the image or what the dog is doing.

For getting a in-depth understanding you can refer to the following resources:

http://neuralnetworksanddeeplearning.com/chap6.html

http://cs231n.github.io/convolutional-networks/