The easiest and strongest connection, is called a Heated Twist, and is used to connect your snap, swivel, lure, etc.
Run the leader through the eye of the swivel, etc, fold it over and make 5 turns, as if you were making a Clinch Knot, while holding the twists tight, melt the coating with a lighter. It will bubble up quickly, so as soon as this begins to fuse, remove the heat immediately. Snip the tag end of the leader with a cutter, and you are ready to fish.
The snap or swivel should be held lightly in a pair of pliers, and the twists should be made so there is enough of a tag end to keep you from burning your fingers.
I either rig the leader with a swivel on one end and a snap/lure on the other. Or I put a snap on one end, and tie the leader to my mainline with an Albright. The Albright is tied just as you would with mono. Just fold the material over, and lightly crimp the loop with a plier to hold it's shape.
Be careful not to crush it into a tight "V", you want a tight "U" shape to the bend.
The other knot you can use to tie direct, is The Figure Eight Knot.
Google it, it is tied the same way in any material.