I do it the same way as Harley Bob, but I use a Reel-E-Good line winder with extra spools. After I wind the fly line and then the backing onto the reel I unwind the backing on one spool and the fly line on another. Now that the reel is empty I tie my knots and wind the spool of backing onto the reel and then the spool of fly line.

Neither the fly line or the backing get tangled up and it doesn't take long to do it at all.

It is also great for cleaning fly line and applying dressing to fly lines.