I've been line drying since October. Not sure yet how our hot, humid summers will affect it, but my next door neighbor line dried all last summer outdoors.
I have 5 kids. Here's what I do to keep it simple:
I sort laundry into two groups: warm (exercise clothes, underwear + socks except wool or bras), and cold (everything else). As soon as I have enough in a pile to do a load, I do it. That means I do a load or two 4-5 days a week, but then I don't have a huge mass of clothes line drying at once.
Previous owner strung a bunch of lines in the basement next to laundry area. I use those but if I was installing something myself, I'd choose a rigid thing like electrical conduit. I hate the way lines sag. Everything that can get hung, gets hung. This includes boxers and towels/cleaning rags. For small stuff like socks and underwear I made a "rack" by putting a broken window screen suspended on egg cartons on top of a folding table. Works great.
I put a box fan tilted at about a 45 degree angle at one end and run it, pushing the air towards the furnace. Furnace fan runs all the time to circulate humidity. The fan part isn't strictly necessary, but it cuts drying time in half. Most of our clothes are dry in 12-24 hours. Jeans take 2 days solid.
As others noted, not only do you save on the cost of running the dryer, but clothes will last (on average) 200 wash cycles instead of only 100. Also, since all of my dress clothes are wrinkle free, they line dry perfectly - they actually look BETTER than using a standard dryer. If you need your stuff to look totally crisp/pressed, you'll still be using an iron, but they meet my standards.
It takes extra time at first, but I find the 5-10 minute breaks it builds into the day between homeschool lessons and other stuff is actually kind of nice. Gets me out of the desk chair and moving.