I've done cloth diapers for a few years now -- yay, cloth diapers! There are lots of different ways to go about it, depending on what is the most important to you -- cost, convenience, all-natural?
We use a couple of different cloth diaper solutions in my family, depending on the day and situation. On regular at-home days, I use cotton flats with pins underneath knit wool pants (or shorts in the summer). The diapers are a great big square of hemmed cotton (sometimes sold as dish cloths or flour sack towels). They are easiest to wash by hand compared with prefolds (though I use those as well), but need to be doubled up for a heavy wetter. My pins are stainless steel, and they are the best closure system that I have tried yet. The best part of our diapers are the wool covers -- they are so cool! 100% wool, treated with a little bit of lanolin (natural oil produced by sheep) every time I wash them. The pants keep the moisture in while the baby runs around, but totally breathable unlike plastic covers, and super soft (not scratchy like I originally thought would be the case).
The pros of diapering this way are that everything is all-natural (something that was important to me), the diapers fit from day 1 until potty-trained (unlike sized diapers), diapers wash more cleanly than others I have used, and I just like that way they feel against the skin. Also, if you are creative, you can do this kind of diapering for very little cost. The cons are that the wool diaper covers must be hand-washed, but only once a month or so. There's also a bit of a learning curve to getting a good fit, more so than other kinds of diapers, but I find that it's easier to get a customized fit with fewer leaks with this diapering system than many others.
For cost savings, I made my own wool covers. Some are wool sweaters from the thrift store that I cut apart and sewed into pants. Some, I bought 100% wool yarn at the craft store (Paton's classic wool is my fave) and knit and crocheted my own wool pants from free patterns on the internet. To make your own diapers, I recommend buying thrift store sheets (or upcycling some old ones around the house) and cutting them up into rectangles and hemming them with a rolled hem. This is the only cost-efficient way to make them, as new fabric costs for high-quality cotton (not quilting fabric) can be prohibitive. I also made my own cloth wipes using flannel receiving blankets (two layers, rolled hem).
We have many more diapers than we actually need. To start, I would say that you
should have around 2 dozen diapers, and 4 wool covers. I alternate between 2 wool covers during the day (hang one pair up to dry while the baby is wearing the other pair), with two back-ups. We wash diapers around every 2 days. I do a cold rinse, then a hot wash with our ordinary laundry
soap (around 2 tablespoons for a full load). One more rinse, with 2-3 tablespoons of borax in the water to help get things really clean. Then hang in a sunny place to dry (or our indoor line during inclement weather). To wash the covers, I rinse in warm water and then I pour a combination of melted lanolin and soap into the water and let the covers sit for a few minutes, rinse with clean water, squeeze out excess moisture, and lay flat to dry (drying takes a full day or two). I only wash covers about twice a month, or whenever they get soiled. The pins, I keep in a cake of soap to help them to slip through the cotton diapers well, and I sometimes sharpen the ends with an emery board. Sharp pins are less dangerous than dull ones.
At diaper changes, I just wet down a dry flannel wipe with some warm water, clean what I need to, rinse solids in the toilet, and throw the diaper in a pail with a lid. If the baby is a bit rashy, I apply some coconut oil to his bum before putting on the clean diaper. If his wool pants are a bit damp, I will turn them inside out and put them back on (they are reversible) or put on his second pair over the clean diaper.
So that's how I diaper, in a nut shell. Good luck with finding what works for you!