I think that this is the #1 concern for people when it comes to cloth diapers. The thought of having to actually dispose of baby poop properly rather than just throwing it in the trash can be really daunting at first, but it's really not a big deal! First, consider this- human waste does not belong in the garbage can, and just because it's "gone" from your house doesn't mean that it is "gone" from the environment. I'm not a "green" person by any stretch, but even I can see that adding diapers full of poop to a landfill is just not healthy for the planet or for us. All of that human waste leeches into our water supply, which is just disgusting no matter how you look at it.
So what are we supposed to do with baby poop? When your baby is a newborn and is eating only breastmilk, just throw the cloth diaper- poop and all- into the washing machine. That's it! Breastmilk poop is completely water soluble, so it will dissolve and wash away with no effort whatsoever. This is also true for formula poop. With formula fed babies, the consistency might be a little bit thicker than breastmilk, but I never had any problems with it rinsing clean. Formula poop also stains less than breastmilk poop.
Once your baby starts solids, it takes a little bit more effort. For the first few weeks after starting solids, look at the sides of your washing machine after you do your initial rinse cycle. Once you notice that the first rinse is leaving, to put it gently, remnants in your machine, that is when you need to start taking extra steps to get rid of the poop. Poop now goes in the toilet, just like yours. If you have modern plumbing, you can use flushable liners for your diapers. These are kind of like rolls of paper towels. You put a sheet in the diaper, and when your baby poops you just flush the whole thing down the toilet. Another option for liners is fleece fabric. You don't flush the fleece, just shake it out over the toilet. Poop doesn't grip to synthetic fabrics as strongly as natural ones so the poop will come off easily. Again, please don't flush fleece liners and don't use flushable liners unless you consult with a plumber who gives you the ok- your pipes may not be able to handle it.
Another option is purchasing a diaper sprayer that hooks up to your toilet. These have a learning curve. Your best bet is to start off with low pressure until you figure out how to use it. I've never used one because I think that I would probably make a huge mess with it. You can also buy a plastic spatula and scrape the poop off into the toilet with it. Rinse it and store it with your toilet brush caddy. My super lazy method now that my son is on full time solids is to plop off what I can or pick off what I can with toilet paper, then just put it in the wetbag and not worry about it. If it's a big mess, I will spray it with our showerhead in the bathroom sink (and then wipe the sink down with a bleach wipe).
The best part is that there is no need to soak or dunk diapers in the toilet like they used to back in the old days. I've done it a few times because sometimes you will get a really terrible diaper mess and you have this "Oh dear lord, what do I do with THIS??" and I just wanted to get it done as quickly as possible. Rubber gloves will be your friend sometimes. But the way that I see it is first of all, if you have a kid you're going to be dealing with poop and getting poop on your hands no matter what kinds of diapers you use. It just happens, it's the way life works when you have a baby so get used to it. Second of all, you're going to wash your hands after you're done changing a poopy diaper, so does it really matter?
I don't think that I've ever typed the word "poop" so many times in one document before in my life. Motherhood.