...things my mom taught me about fly fishing:
Checking the line...
You feel micro-grit on the line as you strip it in
For floating line, the first 10 feet or few meters of line doesn't float any longer
The line retains coil memory
The line has small cracks
The line feels brittle
Draw about a gallon or a few liters of hot water in a sink
Add just a few drops of mild dish soap. Don't overdo it! All you need is enough to make a few bubbles and help loosen debris. Too much soap will leave a film on the flyline which may help it sink. (not good for floating lines!)
Strip out all the flyline IN LOOSE coils in the sink, ensuring each coil lies on top of the previous. This will help prevent the line from knotting up as it is cleaned in the next step
Allow the line to soak until the water becomes luke-warm; about 15-30 minutes or so.
Stretching the line
Stretching the line is an important step in cleaning it. Stretching the line once-in-awhile helps maintain its suppleness and prevent line coil memory.
Taking a clean, moistened rag in one hand, draw the flyline from the sink through
Apply mild pressure with the hand holding the rag to ensure the line is being "stripped" of all the debris and dirt
You'll know if you have enough pressure by hearing the line "sqweek" through your hands
LOOSELY coil the line on the floor at your feet in preparation for dressing the line with conditioner and allowing the line to dry for a few moments
TIP: as you draw line through the rag, stretch each arm's-length section as you would a leader, to stratighten out the coils that have built up.
Using the reel as a line winder makes applying line conditioner easier, but is not necessary.
Taking another dedicated rag used for applying line conditioner, soak the rag with conditioner
As the line is wound on the winder, apply the line conditioner in the same manner as the line is cleaned in the step above.
Don't be afraid to be generous with the line conditioner; it's the stuff that will help protect the line in future uses.