It seems that many people have difficulties with storing line-sets for 2 line, and especially 4 line, kites. This is an area which can make flying a most pleasurable experience, or a real "pain in the butt" - I'll try to ensure that you experience the former.

Though you "can" get into a terrible mess with lines, I've never really had much of a problem, perhaps I'm lucky, perhaps I just have an affinity with "bits of string" - who knows? Either way, if you use the right equipment, have a little patience and a willingness to learn - there's no reason why you should suffer serious problems. None of what follows is "written in stone" but in my opinion - it should be :-)

"The Equipment"

First of all - get yourself a plastic "figure of eight" winder.
These are cheap enough, and available at every kite shop I've encountered to date (note I said "kiteshop" not "model shop" or "toy shop" in my experience such places are overpriced and supply little of real use to the kiteflier). Nothing equals a "fig8" for multi line storage - I don't care what anyone says.
Having got the line on the winder, you'll want a method of keeping it there - I use a piece of thin "bungie cord" 8 inches long with a knot at each end - high tech or what!

The lines themselves - I'm assuming that you'll be using some form of "Dynema" lines, with the ends "sleeved and looped".

To make life a little easier, all my "quad line sets" have an overhand knot at the end of the loops more of that later).

"The Method"

1. Ok, you've finished flying and want to go home - I'll deal with 4 lines, 2 will be the same - but simpler:
   Begin by removing the kite from the end of the lines, remove the top-right & bottom-right lines from the kite and "larks-head" one onto the other (using the overhand knot mentioned earlier) - do the same with the other side. Pack the kite away or, using a ground-stake, fix it to the ground so it won't wander off by itself. You now have two pairs of lines on the ground, their respective ends joined - leave them a yard or so apart to avoid confusion.
2. Walk to the other end of the lines, remove your flying handles and join the lines in the same way as before (and the same pairs!) You now have two "joined pairs", on the ground, lying straight and parallel to one another.
3. Now for the "technical bit".
   Take the winder in your left hand (I'll assume you're right-handed), you should find a small slot (or two) at one end of the winder - this is you're starting point. Pick up the end of one line "pair" and lock it into the slot using the knots you'll have on the end. Pick up the other pair and do the same (same slot or other slot if you have two). Avoid crossing or twisting the pairs when doing this.
4. Right, keeping the winder in the left hand - separate the four lines between the fingers of your right hand (you should just have enough fingers). Now, without changing your grip on the winder or the lines - begin to wind in a figure of eight fashion. Yes, I know you seem to be twisting the lines as they go onto the winder - the good news is, the twists actually help the process!
5. As you wind the lines in resist the temptation to drag the line towards you - this will definitely create twists and tangles!
   Walk slowly "into" the line, timing your steps so that you neither pull line towards you, nor "overtake yourself" so to speak.
6. When you get to the end, as the separated pairs come together at the winder, make sure that the pairs remain separate as you place them neatly, one at a time, into the same slot that you started with.
7. Use your "bungie" to hold the whole thing together - it's best to then place the lineset in it's own small ripstop bag for storage. Done, now go and have a sit down - happy in the knowledge that you'll have no problems next time out!

"Next time out"

1. So, the sun's shining, the wind's blowing (a very rare combination where I live) and you're off to fly:
   Lay the lines out first. Take your ground-stakes and fix the ends of the two pairs of lines to the ground, a yard apart, after carefully removing them from the winder.
2. Poke a finger through the large hole in the centre of your winder - and stroll slowly downwind, whistling happily to youself........
   You'll probably have to assist the line as it leaves the winder to avoid any problems - but whatever you do: Do Not Remove That Finger or turn the winder at any time!
3. Continue until you reach the end of the lines, carefully separate the two pairs, drop the winder and gently tension the lines. You'll find perhaps a twist or two between the pairs of lines, but no more.
4. Having separated the pairs, you may now lay the lines on the ground, walk back and pop the handles on the lines, drop the handles over your pegs, then set up the kite for takeoff - and away you go!

For twin lines - do as above but don't bother with the overhand knots in the loops, just pop the two loops over the end of the winder and wind. Treat each line as a pair for the purpose of reading the above. Easy!