Surgeon's Loop
The surgeon's loop is the fastest loop knot in fishing. Tie it in the butt section of a leader so you can swap leaders without retying every time. Pair it with the loop on the end of a fly line for a no-tools connection.
Tying it
1. Double the line back on itself, about 4 inches of doubled line.
2. Tie an overhand knot in the double, leaving the loop hanging open.
3. Pass the tag end (which is now a doubled tag plus a single tag from the loop) through the overhand a second time.
4. Wet. Pull all four strands evenly. The loop seats.
5. Trim the tag.
Sizing the loop
A loop the diameter of a quarter is the standard. Smaller works for thin tippet butts; larger handles heavy braid. The loop has to be big enough that the corresponding loop on the fly line passes through cleanly.
Loop-to-loop connection
Once both ends have loops:
1. Pass the line-end loop through the leader-end loop.
2. Pass the entire leader (fly and all) back through the line-end loop.
3. Pull. The two loops draw against each other like links in a chain.
This is the strongest connection in fly fishing. It's also reversible: no knot, no scissors.
Caveats
The surgeon's loop is weaker per knot than a perfection loop. If you fish for steelhead or trophy browns, take the extra 30 seconds to tie a perfection. For panfish and warmwater bass, surgeon's is fine.