Create a new document, preferably of size 900x800 (will be easy for beginners).
Draw a rough sketch of any (furry) animal.

Create a new group and call it "Base"
Create a new layer and fill it with your desired color: that's the base color.

Duplicate this layer and call it "Noise".
Go to filters and add noise.
Amount : 12-14%
Distribution : uniform
And make sure that the monochromatic box is checked.

Duplicate the "Noise layer"
I duplicate my layers a lot... So when I mess things up I always have something to fall back on.
Brush type: spatter
Size: 40-60 px(depends on the area you are working)
Mode: Normal
Strength: 70%
and smudge it in the directions of the fur. There's nothing wrong to use some references to know how the
fur flows.

Now use burn and dodge tools with the below settings.

Create a new group and call it "fur"
I am really bad at naming my groups and layers;-)
Create a new layer and call it " A"
I hid the "Base" group so that you can see what I have been doing.
With a darker shade of the base color make some brush strokes... don't forget the flow of the fur.
Use at least 2-3 dark brown shades.

Create a new layer and call it "B"
Similarly with lighter shades(2-3) of the base color make some strokes.
Play around with opacity(30-45) ,flow(40-50) and brush sizes(3-5px).
For really fine fur use a brush of size 1-2px.

I revealed the "Base" group, so the image looks some what like this:

Create a new group and call it "Nose"
Create a new layer and call it "c"
Set the foreground color to white and paint it.
Use spatter brush to smudge as shown.

Create a new layer and call it "D".
Draw basic shape of nose.

Create a new group and call it "ears"
Drag this group in between the "Base" group and the "fur" group.
Create a new layer"E"
Used few shades of pink for the ear.

Right ear

Create a new group and call it "eyes".
Create a new layer and call it "F".
Select the eye and apply gradient.

Use dodge tool

Draw some fine lines as shown

Smudge the lines

Create a new group call it "Mouth".

Added some shadows and fine fur

I am a right handed person. So drawing strokes from left to right comes with a little or no effort. If I need to stroke in any other direction I just rotate the canvas accordingly.
Added whiskers

If you have patience you could paint the whole face the same way as we did the fur on the forehead.
But I dint have the patience so I merged Base and fur groups.
Copied ,pasted ,rotated and warped according to the shape.

It looks very sloppy but don't worry all we need to do is finish it off.
1) Erase the edges and smudge
2) Ears(played with colors of the right ear to make sure it doesn't look exactly like the other one)
3) Added individual strokes of fur.

Final result