For trout fishing: If your knots are AWESOME, and your fishing spooky fish then flurocarbon is great. However, my knots are NOT awesome, and therefore I also lose fish with it (at the knots), so I prefer mono tippet. The problem with mono is that it degrades reasonably quickly (fluro lasts forever), so you need to replace your spool every couple of years.
For fly line to leader, I use a loop to loop connection (with a perfection look at the butt end of the leader (if it doesn't already come pre-made)
For leader to tippet, I use a TRIPLE surgeons knot or a blood knot. I find that a DOUBLE surgeons don't hold very well. Triples seem to work well with light tippet material (5x or 6x).
For steelhead and salmon: mono - flurocarbon isn't needed and is a waste of money