First and foremost, read the manufacturers recommendations on line care!
They know what's best for their lines and it is in their best interest to have you get good service and performance from their lines. If they mention using their condititioner, it's really cheap insurance at $3-4.00.
No detergent! The makers will tell you that. It leaches the plasticisors that make lines slick.
Modern lines are so slick and carefree that I would even try to see how long I could make an old-school line last. The difference between the old lines and modern lines is night and day. The new lines slickness repels dirt and grime and if they do get scummy they are easily cleaned as suggested by Sandfly.
As for the 3M/SA micro-abrasive cleaning pads for lines with built-in slickness like SA with AST, Wulff's J3 and Rio's coating, a swipe or two bring a fresh surface to the top. The pads are like 12-1600 grit sandpaper.
To answer Clint's concern, and because I'm in the metrology field, I once took a .00005" mic to a section of line and it must have taken, honestly, 50 swipes with the pads before I noted a difference in the line diameter. When they say micro they must mean it!
What a time to be a fly fisher though. It seems all manufactures have caught on that the very least we expect of a floating line is that it float! Rio caught on early and now the others have followed suit. SA now uses the tiny loops on the ends of their premium lines that not only seal the end but doubles the floatation in that critical area. Cortland does it best though. Their Dyna-Tip lines somehow miraculously float without the loops and without making the end-user jump through hoops by sealing them.
Aside from skill, the line is the most important part of the whole game we play. The right line will wake-up even a marginal rod whereas the finest rod with the wrong line just doesn't cut it.