Here's how we cloth diaper on the fly:
First, I chose a diaper that was easy to work with. In my case, a pocket diaper made the most sense -- they are as convenient to use as a disposable (they go on and fit the same way), but unlike the all-in-one diapers (which are really the most convenient because all they require is laundering) they dry much faster after washing because you separate the absorbent inserts from the pockets for laundering. That means you don't have to have as many of them (if you hang them to dry) and/or you don't have to run your dryer for as many cycles.
For us, I chose the BumGenius 4.0 one-size pocket diapers. I purchased a few of them from Target.com, a few were given to me as gifts (the advantage of Target is that you can put them on your baby registry!), and the bulk I ordered from cottonbabies.com . They retail for about $19 per diaper, but I've bought them for as little as $12 per diaper on clearance. It's an expensive initial investment (you need about 24 diapers to make sure you don't run out while you're doing laundry), but given that you save about $1500 to $2000 over the diapering life of your child by choosing cloth, it's well worth it. They come in two closure types, snaps and hooks-n-loops (i.e. velcro) -- I discovered that the hooks-n-loops fit my baby better than the snaps (she has a big belly and skinny little legs). However, most folks I've spoken with prefer the snaps due to their better durability. But I'm only going to have one baby to get through with this diaper stash, and am perfectly capable of replacing velcro strips if I need to, so this will work out just fine for us.
Here's how they work: You pull out the inserts and unsnap all of the snaps to launder. Here's a pocket and an insert with none of the snaps fastened -- this accommodates the largest babies and will be how we'll use them when Rosebud is much, much bigger.
We launder our diapers at night -- we run them through the washer with a pre-wash cycle and an extra rinse cycle (our front-loader can be programmed to accommodate the extra cycles, it adds about 25 minutes to the regular cycle), then the inserts go into the dryer (normal cycle) just before bed, and the pockets get hung on a drying rack. By morning both are dry and ready to be assembled for that day's use. I put them together while I nurse Rosebud in bed when she first wakes up in the morning.
The first thing I do is to snap all the snaps to the right size. This is at the smallest setting currently (and will be for awhile) on both the pocket and the insert. Snapping all the pocket and inserts takes about two or three minutes.
Then I stuff the inserts into the pockets. This takes a little longer, but I can get them all stuffed in about 15 to 20 minutes. I'm stuck in bed anyway while Rosebud nurses, so it doesn't really matter.
After a diaper is stuffed it looks like this, then I fold it up like in that first picture above and stack them all in a bin. Then they are ready to be grabbed and used, just like a disposable.
One more thing, just before putting a diaper on her, we lay a Mio disposable liner inside the diaper. (They come in packs of 160 for about $9, we bought ours from Target.com.) This liner catches the major poopy chunks and can be lifted and thrown out, leaving the diaper ready for laundering without any other treatment. (And with WAY less trash generated than tossing out a disposable diaper.) This is what makes the whole thing really doable and simple, and is what convinced me that we really CAN cloth diaper despite such a busy on-the-go lifestyle. I just stash the dirty diapers in a waterproof bag, then turn the bag inside out into the washer (and toss the bag inside too) at laundry time.
Cloth diapering saves money, it's healthier for the baby (no icky chemicals in the diapers), and it's better for the environment.
And they come in such scrumptious colors, too: