While there is no one "correct" way to rig a rod and reel outfit, the methodology I employ evolved in the crucible of the salt flats to be flexible and as failure proof as knots tied by man can make it. It might be considered a little overkill for trout fishing but I don't believe so and set up a 4-weight system the same way as a 10-weight outfit.
I use a modified arbor knot to affix Micron backing to the spool. doubling the backing into a 3 foot length, I then tie a surgeons loop. at the tip of the loop I tie a second surgeons loop as tiny as possible. I run the long loop around the reel's arbor twice then, again using a surgeon knot rather than an overhand, encircle the standing portion of the doubled backing and snug it down. All this doubling and use of the surgeon rather than typical overhand knot make this attachment to the reel less likely to slip and stronger than the backing itself should a bad boy ever take you to being spooled.
Wind the backing under some pressure to be as tight and uniform as you can get it and, again doubling the backing to a 4 foot length, do a 48 turn Bimini Twist. Most fly line today come with a factory welded loop on both ends which is very slick and neat but, being a thermo chemical bond, is about 80% the strength of the fly line itself which is 20 to 30 pound test in most instances. I mechanically re-enforce this loop by wrapping a 12 to 15 turn nail knot of 20 lb. fluorocarbon tippet material over the doubled portion of the factory formed loop making it stronger than the line itself. Passing my Bimini through it and over its plastic spool, loop the fly line to the backing. Reeling the line onto the reel it should nearly but not quite fill the spool. There must be a little free space as when fighting fish you may not get your line back on as neatly as executed in your living room and you never want to jam a reel pillar with too much or uneven line! By loop-to-looping your line to the backing, it is simple to wind the line off the reel and back onto its plastic spool should you wish to mount a different line on the reel.
There are a variety of variables involved in attaching a leader to the line: Will you use prefabricated, extruded knotless leaders, hand built, furled or braided butts? Each has special requirements. One thing all have in common is they must be mass-matched to the fly line to assure effective transfer of energy from your cast to line to leader. This is easily tested by performing the "Parabolic Loop Test". Again, a re-enforced factory welded loop can be used to loop on a commercial, pre-perfection looped leader...I don't think too highly of most of these, your own hand-built leader which are always a good option, or a correctly line size matched furled or braided system which offer improved dry fly presentation performance. With the braid I prefer to sever the loops and do a "Chinese finger cuff, Zap-A-Gap splice". Loop forming alternatives are thoroughly dissected in a thread searchable in Tackle, Welded Loops in the appropriate section of this Forum.
The Parabolic Loop Test verifying optimal transfer of energy, in this case with a Cutthroat, line sized matched, Hybrid Furled Leader
A perfection loop is plenty strong for the butt of a mono or fluoro leader being it is generally in the .024 - .021 diameter range. A popular alternative is to multi-turn nail knot a section of butt material to the fly line and tie a perfection loop in it. Build down using blood knots, the strongest, straightest and most elegant leader knot.
I like long tippets, 5' trout fishing and 3 to 4 feet in the salt. My favorite tippet to fly fixed knot is the Trileen Knot, similar but stronger than the clinch, it features passing the tippet through the hook eye twice so it is not merely stronger but it locks on the front of the hook eye maintaining proper attitude. For flies that will be stripped and paused, streamers, buggers and most all saltwater prey imitations, the Non-Slip Loop Knot is strong and affords more life-like freedom of movement as your fly wafts down on the pause...this often when the striped bass or bonefish eats.
There are a number of knots employed in rigging. Do not be intimidated by them they are all easy to learn and repeated use will make you a master. It is a traditional aspect of being an angler that you are skilled at knot tying. Today's internet videos and step-by-step animations make learning knots easier than ever and, with the exception of the Nail Knot which is best tied using a thin tube, all the other knots mentioned here are tied with the best knot tying device in existence...your hands.