I use one of two brushes in Photoshop. The variety of speckled brushes and the brush mode Dissolve. It makes splattered dots I can smudge, but that lacks details I just add in with the speckled brush and a fine brush for more details. I don't think it is has a lot to do with details as it does with hair directions and stroke appearance. You can do it the hard whay or you can create a style of doing the same look. Pixels create an illusion that looks right. How you get that is up to you, but for me, the easiest way is quicker and it does the same thing. The only difference is experience.
It's hard to gauge your style with only the single piece but if you want simple, cartoon-style art, simply adding some texture through simple highlights/shadows in the fur itself is enough to get the point across.
Here is a hair tutorial (cel-shading) that demonstrates the effect:
Probably the best (although not the fastest, unfortunately >.<) is to just get in there are start practicing lots and lots of fur from reference (or life, if you have a fluffy pet or furry jacket or something). Otherwise, searching up "fur tutorial" might give you some interesting ideas for what technique you want to use ^^
I would mention, I don't think every strand is necessary unless you're aiming for a hyperrealistic macro look. A lot of artistic decision is put into translating the literal visual information into a 'readable' format. Sir Edwin Landseer likely did not set out to paint every hair on these pups (although he could suggest texture with brush techniques), but I don't think anyone would mistake the dogs for being anything but furry. [link] The further you get into impressionistic or symbolic styles, the less important "every strand" becomes, and instead the "idea" of fur takes it's place.
A skin tutorial also once mentioned, and it is usually true, that texture done in the highlighted regions can give the impression of an overall feeling of texture.
His "the human is about to take a picture of me" sensors are very acute. The second I even reach for my phone, he suspects something and stops doing whatever funny/adorable thing I wanted to take a picture of. Oh, cats.