How I do this is to actually load the reel I'm going to use in reverse to start. That's right, first I load the fly line onto the reel, then I attach the backing to know how much is needed to fill the reel spool. Then I put it all onto a spare spool, or anything I can wrap it all around. I do this a couple of times to get the backing to the front & then load my reel.
What's good about my method is that you can do it anywhere, say, at a picnic table along the stream for example & you don't need any fancy equipment. What's bad about my method is that it's time consuming.
The video below demonstrates a better method, though you'll need a few tools for it. If you're doing this at home that should be no problem & the method shown below will really save you some time. This is especially good if you've got more than one fly reel, or spool, to do in the same session. It will really save you some time & - with some modifications - will work on any fly reel.
(Note: we'll look at the special knots you need to use for fly line & backing in a later post)