To begin with, it would be nice to be able to draw at least something at all ... If this works out, then you can think about how to draw animals, which are very numerous around us, and they are very different and not very much alike. The fauna is too diverse, but worth a try. This is, at least, interesting and informative.
How to draw animals?
In short, with understanding. And the goal we want to achieve, and the graphic techniques that will help us do this. This is necessary in order to be able to later explain how to draw animals to children when they ask about it. But in any case - this is an exciting lesson, drawing. And anyone who has such a desire is able to figure out the correct sequence and answer the question of how to draw animals. For example, we will choose a small elephant from the entire diversity of the animal world. Why not? Any drawing begins with the correct layout - you need to broadly mentally imagine the desired result of your work and correctly place your future drawing on a piece of paper. Light strokes indicate the boundaries of the image and some semantic compositional center. In no case should it coincide with the geometric center of a sheet of paper, such is one of the laws of composition.

Next, we perform the construction of the elephant’s figure. Having identified the main volumes in it, we carefully compare their proportions between themselves and the whole figure as a whole. This is the most important moment in the construction of any animal, we will try not to be mistaken. Otherwise, we simply can not cope with the answer to the question:
"How to draw animals?" Having dealt with the proportions, we work out some of the most interesting details that have seemed to us and generalize the drawn. We try to convey the general character, mood and dynamics of the figure. If necessary, simulate the figure and the elements of chiaroscuro. Pay attention to the hatching. It is useful to pre-train and understand the arsenal of expressive capabilities of such a familiar tool as a pencil. Well, almost done ... In the process of drawing you need to be able to stop in time. We can say that, as a first approximation, we coped with the task and answered the question of how to draw animals. But do not stop there.
Let's fantasize
Let's try to depict animals not as our eyes see them, but as we feel from the character. Let it be cartoonish and caricatured. Let's give animals human features. In the world of fine art there are many examples. On this, in particular, the whole animation is based. How to draw cartoon animals?
For this, first of all, you should abandon the desire to depict them photographically accurately. This is clearly not the case. You should start here with the capabilities of linear graphics. The line can convey any character and the whole range of moods. And what matters to us above all is not “similarity”, but expressiveness. This is what one should strive for. And before embarking on a large drawing, it would be nice to look for the desired line on a small sketch. This should be done easily and relaxed.