This is the technique I've been using for some time to make paw pads and it's my favorite since it comes out looking like more common silicone pads without hampering manual dexterity as much. For the material I've been using handstands stick pads because I like the texture and it provides some additional grip.

I make a pattern for each pad slightly bigger than what I want the final size to be and cut each piece out of the sticky pad. Once cut out, peel off the backing and position it on the fur. You'll want to use a hidden/ladder stitch to attach the pad. By sewing around the edge it will cause the material to puff out and give it that nice 3 dimensional form.