Using Power Pro Hollow Ace Braid backing these days, so I like to wrap a layer of electrical tape on the core of the fly reel. Since the line is so "slippery" the tape gives the braid something to "grab" on to.
Make sure not to use too thin a braid, I use a 30-40 lbs test braid that has the diameter of 10-12 lbs mono.
Tie a 8 turn UniKnot and cinch up against the core of the fly reel.
One of the most important things about using the super braids for backing is to wind it on the reel under some pressure. For this I use a folded over paper towel that the line goes in and then I weave that between my fingers....
....and if you have a helper have them hold the spool and apply a little pressure as well
The next most important thing is to wind the line in even layers back and forth across the reel.
Don't overfill the reel with backing, but try and get it so that you have just enough room for your fly line. Usually if you fill until there is about 1/2"-3/4" of space available from the backing to the outer "lip" of the spool you will be fine.
Remember, This backing core is what you will use to fight and wind in the fish. So if you under-fill, everytime you turn the handle, you will only bring in that circumference of that core (fly reels are mostly one to one retrieve ratio) To simplify the smaller the core, the less line line you retrieve per handle turn.
Tie a Bimini twist or a spider hitch at the end of your backing. This creates the first loop of a loop to loop system of attaching the fly line to the backing.
Mark the end of the fly line with a "Morse Code" symbol for the weight of your fly line. Here, a seven weight line is marked with one long "dash" and two short "dots" (Dash=5 and Dots= one each)
Make a loop in your fly line and then using a fly tying thread and bobbin, "whip" the thread around the base end of the loop.
Keep rotating the bobbin around the fly line back and forth until you have two layers about 3/4 of an inch in length.
Then "whip finish" the end of the thread back over itself. I use my fingers, but there are tools that do this available from fly tying supply stores. If this proves too difficult, just tie 4 overhand knots back to back.
Coat the wrap with some Plio bond or fly tying head cement and let dry.
Put the backing loop through the middle of the fly line loop and then bring the fly line spool through the backing loop and pull tight.
Wind your fly line onto the reel and attach leader.
For this seven weight, we started with a 3.5' section of 30 lbs. mono tied with a nail knot to the fly line. Then a 3' section of 20 lbs (tied to the 30 lbs with a blood knot), the a 2'5 section of 15 lbs (tied to 20 lbs wth a blood knot) finally a 12" section of 30 lbs shock tippet. This gives you an overall length of 10' for your leader. I will play with the length depending on the situation, longer leaders for spooky fish, ( I use some as long as 14') and shorter for deeper water "unspooky" scenarios (as short as 9')
After all this, you are probably mentally exhausted and wondering what possessed you to take up fly fishing in the first place. But remember once you do this a couple times it will start coming natural. After you put the backing and fly line on once, the only thing you will change frequently is the leader.
An easier way to do this is if you buy the line and leader from a flyshop, most of them will do this for you.
Enjoy the challenge and fun of fly fishing!