I start by attaching a length of 30lb fluorocarbon to make the butt section. I use a modified Albright Knot for this. Basically I tie an Albright, but leave the waste end of the fluorocarbon the same length as the end you would normally leave.
If you don't know the Albright you can find out how to tie it here, just remember don't trim the waste like the standard knot.
The next thing I do is furl the two ends together to make a single butt piece. To avoid putting a ton of twist in the fly line I tighten the drag on the reel and pick up the whole rig. then make sure you hold the fluorocarbon between the thumb and forefinger of one hand so that they can be pulled round each other, then spin the reel with your free hand till the fluorocarbon twists together.
Then make a loop in the furled section. A simple double overhand loop will hold fine.
To finish off I coat the fly line to butt connection with silicone. I use silicone as it's flexible, tough and bouyant. Other adhesives I have found can harden which I don't like. I like this heavy butt section to be about a foot long including the loop.
This makes for a bomb proof butt section which you can attach to your leader with loop to loop connection. I usually only change these once a year unless they get damaged somehow, but they are pretty robust.
As far as the actual leader is concerned I make a step tapered leader from 3ft of 30lb fluoro, 3ft of 20lb fluoro and 5 ft of 15lb. I rarely go lighter than 15lb at the tip, but if I need to I just shorten the 15lb section and add a 10lb tip all connected with 2 or 3 turn water knots. I never fish lighter than 10lb for carp, partly because I fish quite snaggy waters, but also because I never found them to be leader shy. In fact I am much more likely to make my leader longer than lighter as I have found that to make a difference on several occasions.
This is just the way I do thing, and some people might not agree with it. Of course you can just go with 7ft of 8b fluoro straight to a braided loop. I just think the extra effort to make a good leader that will turn over by itself is worth it for the one day it makes a differenc.