For some of you, these knots will not be needed. There are a variety of ways to tie on leaders & tippets & hooks, especially these days. There are some loops that make switching leaders a breeze these days, but it wasn't always this way. In fact as far as I can tell, loops in the ends of fly lines is a fairly recent thing. Before that if you wanted to change your leader you had to tie a knot. Some of us still do.
Obviously these knots are very important. They are where the action is going to be - on your leader, tippet, & your hook. So you want to make sure these are good ones. These ones shown below are time-tested & will hold your equipment well.
The following is taken from a 1982 booklet that used to come in the box with every Scientific Anglers (3M) fly line sold back then. It does a good job of showing & describing these knots.