Tapered Leader

Fly fishing tackle has four parts: backing, flyline, leader, and tippet. You seem to understand backing and flyline. Leader is (as one answerer here on Y!A once put it) the "invisible barrier" between you and the fly. On the end of the leader is tippet, which is more clear line, usually the same linestrength as the end of your leader. Tippet is the "disposable" part of your line -- you use it up tying on flies so that you don't eat into your leader.

You don't have a tapered leader, so you want to make your own. That's great and perfectly do-able. For a beginning fly angler with a 7/8 wt rod, I'd recommend a 7-foot leader, though as you get better at casting you'll want to move up to a 9 or 12 foot leader. So, 7 feet of leader from your line to your tippet. I would recommend that you taper in three steps if possible -- from about 8 pounds down to 4 pounds. If you could do this in three steps, that'd be optimal. The taper allows the energy in your cast to dissipate in a way that straightens out your leader and lets it cast flat out onto the water. If you can taper this in three sections with very small, tight knots, I think that'd be best -- 8 lb., 6 lb., 4 lb., in roughly 2.5-foot lengths.

To join them I'd recommend a surgeon's knot:

http://www.animatedknots.com/surgeonsjoin/index.php

If there's any way you could get some "real" tippet (about 4x or 5x) , I think your experience will be better. Get tippet that is the same linestrength or slightly lighter than the line at the end of your homemade leader. If you can't get real tippet, just use another 18-inch length of 4-pound test for your tippet. Use this to tie on flies, and when you run out, tie on another length. That way you don't use as much of your leader.

This will get you started, but be advised that using "real" leader is much more satisfactory. It tapers evenly, gives you better distance, and will not have knots that may spook or distract fish.

One more thing -- your leader will look like a big slinky after it's been on the spool and then on your reel for a while. In spincasting you don't care much about line memory -- you just let it work itself out as you cast and retrieve. In fly fishing, you want to get that memory out of the leader BEFORE you fish. Pull the leader through your hands a bunch of times to warm it up and ease that memory. You want it nice and straight with no loops or coiling in it. You can also pull the line through some cloth (like a pinch of your shirt or vest), and they even make a little gizmo made of leather that does the same thing.