I am a little confused by which backing you have Cortland makes a Micron backing and a Micronite Super Braid Fly Line Backing. I am going to assume that it is the Micronite Super Braid. With the super braid lines you get two items you have to deal with. The line is smaller in diameter and is more slick. The slickness of the super braids makes your knots more important. Sometimes knots that work with mono don't work as well on super braid.
How to fasten backing to the fly line
A very good way to tie backing to the fly line is with an Albright Knot. Here is a link
that shows how to tie an Albright Knot. Use the 10 to 12 wraps and you won't have to worry about the Albright slipping with super braid. The Albright Knot should be finished with a lock but the tutorial doesn't show one. I usually don't use the Albright unless I am tying to a loop.
You can also use a Nail Knot and I like this option. Here is a link
on how to tie a Nail Knot. If you have super braid I would use more wraps than what is shown. I would use eight wraps or so. Or, you can tie a normal Nail Knot and apply Pliobond or Goop. The Pilobond is probably a good idea either way.
A third option to fasten the backing to the fly line is to form a loop on the end of the fly line. The running line on a fly line is not very big and you can double over the fly line to form a loop of any size. You have to serve (wrap the doubled over line with thread) and apply Pliobond or Goop. Once you have a loop on the fly line you can use an Albright or fasten loop to loop. A Bimini Twist is a very good knot to tie in the backing. Here is a link on how to tie a Bimini Twist
. The Bimini Twist is used mostly for saltwater but it is useful for lines 6wt and above. It is a bit of overkill on a 6wt line.
How to fasten a braided leader to the fly line
You apparently don't have the newest Ridge line. I think the new ones have loops on both ends. This would simplify your problems.
The best method I think is to tie on a short section of 20lb to 25lb mono on the end of the fly line using a nail knot. Then tie a loop in the end. I have always used a Perfection Loop but I think a better knot is the Non-slip mono knot. Use 4 wraps with the 15 to 20 pound mono. Here is a link on how to tie the Non-Slip Mono knot
You can also form a loop like we did on the backing end of the fly line. You might find this too bulky.
If you want to try the braided loop that came with the fly line, here is how to do that. You need to feed the loop onto the fly line end. Some of the braided material may be frayed and you can trim that up. You need to serve the braid and some of the fly line to have a smooth transition. You need about 1/8 on the fly line and 1/4 to 3/8 on the braid. Cover the thread with Pliobond or Goop. I like Pliobond as it doesn't get as hard as Zap-A-Gap or other types of super glues.
Here is a second way to attached the braided loop. Thread the braid onto the fly line like before. Instead of serving the braid to the fly line, tie a Nail Knot at the junction on top of the braid. Pull it as tight as you can get it and trim off the ends. Cover the Nail Knot with Pliobond and you are good to go. If you want a really neat Nail Knot use some of your braided backing to tie the knot.