I literally did this yesterday for the first time. It wasn't pretty but I did some research and this seemed to be the best way for my model. I'm sure with practice it will look nicer.
What is your model made of? I have a wire armature with epoxy 'bones', wrapped in teflon tape and built out with foam. I bought some brush-on latex (local art store didn't have any, but they told me where I could buy some from a modelling specialist in the area). I coloured the latex with a small amount of acrylic paint and brushed small patches on to the model. I then stuck clumps of fur (either lying flat or upright, depending where it was on the body) into the latex and let it set for 24 hours. I then went and filled up any gaps with for latex and fur. I'll post some pics soon and link here. Would love to hear from anyone with more experience to see if this was the best way?
Here's some pics Lola the dog