use some denatured alcohol, q-tips, paper towel or old bath towel you dont use. make sure you take the gears out.

fill the diff a little past the cross pins (gears have to be in). fill it about 80% full, which is basically just a little over the cross pins. when you first start to fill it up, put in a little bit, then rotate the gears so that the oil fills in the air pockets. then fill it the rest of the way.