When tying knots for fly fishing you will find that it requires approximately 5 knots. First you need to attach the backing line to the reel, then the backing line to the fly line, the fly line to the leader and the leader to the tippet. The final knot is used to attach the fly to the tippet.
Backing line to reel - Arbor knot
Most fly anglers use the arbor knot for this application as it is easy to tie and strong enough for this application.
An instructional video of this knot can be found at my earlier post how to tie an arbor knot.
Backing line to fly line - Albright Knot
This knot is often used to attach two lines of different diameters and is perfect for attaching fly line to the backing material.
1. Loop the heavier line. Pass the lighter line around the formed loop. 2. Make approximately 10 wraps with the lighter line wrapping from left to right. Hold these wraps in place. On the 10th wrap, come around and then through the remaining loop. Taking the standing line in your right hand pull gently as you push the wraps with your left hand towards the closed loop, keeping the wraps together. Pull the tag tight then pull on the standing part of both lines until the knot is secure.
3. Trim the tag ends of the knot.
Fly Line to leader - Nail Knot
Some fly anglers continue to use the albright knot for this situation, but I find the nail knot to have a smoother finish - try both and see what works best for you.
An instructional video of this knot can be found at my earlier post how to tie a nail knot.
Leader to tippet - Surgeons Knot
This knot is very easy and quick to tie, but is also sufficiently strong in this situation.
Instructions (with diagrams) for the surgeons knot can be found at my earlier post how to tie a surgeons knot.
Tippet to fly - Improved clinch knot (locked blood knot)
The last knot you will tie and arguably the most important. Most anglers use an improved clinch knot in this situation and it is a great knot for this situation. Remember that you will be using this knot the most and it is the most important to learn properly.
You will find instructions for the improved clinch knot at my earlier post how to tie an improved clinch knot.
I hope this little post helps you with your fly fishing knot tying and your fly fishing in general! Good luck!