How To Draw Cute Dog 1.0

The best way to start is by looking at the outward lines of the animal, and then trying to get them on the paper, and don't start shading and all that until you are satisfied with the proportions are right. A lot of the times it is better to not draw the hardest part of the animal at this early stage, instead focus on the easier parts first. This way you will not get discouraged as easily.
So starting out, just look at the animal reference picture for a while and then start drawing some thin lines that are easy to erase. And do not start shading and all that until your are fully satisfied how the lines look, because once you start to shade this is harder to erase later on.
When you are happy with the general proportions of the animal then start to work on the shading. One hint here is to start at the left upper corner if you're right handed and move slowly to the center area, because that will help you not to get the whole drawing messy with your arm over the painting.

When you think your drawing is done, put it away and do something else. And perhaps the next day or so come back and look at it. Doing this will probably make you realize a few mistakes on your animal drawing that you didn't notice while working on it.

Lastly, remember that you don't need tons of talent to make a great animal painting / drawing, because patience is everything!