There are so many ways, David. I have used micro Drennan rings, even, tying three knots to each (worked, but not highly recommended.)
The two knots I use now are the double overhand knot and a dropper loop. It is almost impossible to explain how to tie these in a post, so I think I will try to get an article done in due course. Or you could, in the meantime, look them up in a book.
The dropper loop's the easiest to tie, but the double overhand knot's the strongest. Both REALLY benefit from a dab of knot glue.
Tie a grinner knot, which is the sort that you use to tie two sections of line together.
Cut off the loose tag pointing up towards the reel. Cut the remaining tag, which points towards the point end of the leader, to a length of about 6 inches, and tie the fly on it.
Fishing with droppers can be a pain, especially on reservoirs with gusty winds. I tend to avoid them unless I'm fishing rivers, when I will use a team of three flies (two on two droppers, the remaining one on the point).
Another knot you can use is the Cove or Surgeon's knot.
At great risk of having blindness pointed out to me, Sean, I can't see the cove/water knot in the link you supplied, though I love the way it shows how they're tied.
Incidentally, the dropper loop is almost identical to the blood knot except that in the dropper loop, both 'ends' (in this case a loop) pass through the same side of the twisted section. I don't use it as a loop; I just cut the loop close to the knot so I get a dropper.
Using rig glue or superglue, if you leave a longish 'tag' end, this can be glued along to the dropper end to get greater dropper stiffness, if that makes sense. I think because of the way it's tied it's not as robust as the blood knot if you don't put a dab of glue on it; not really a great hardship. Indeed, tieing a few leaders at home isn't a bad idea if you really want great knots.