Besides the obvious answer of "diapers," what do you need to get started cloth diapering? Really, just the diapers and a way to wash them is all that's necessary. Oh, and a baby to put them on! Otherwise we get into creepy adult diaper fetish territory, and no one wants that. I hope.
There are, however, many things that will make your life easier. (This is accessories only: diapers, inserts, and covers are not included here.)
1-2 small wetbags for the diaper bag/going out. Two is nice so you have one available while one is in the wash but not necessary.
A place to store dirty diapers. You can get a special diaper pail, but really all you need is a trash can with a lid. The more air circulation, the less smell, so a swing-top lid is a good bet.
1-2 pail liners. Two is nice so you have one available while one is in the wash, but not necessary. You put the pail liner in the trash can or diaper pail. It allows you to transfer the dirty diapers to the washer without having to touch any dirty diapers (just turn it inside out into the drum of the washer), and can help contain smells.
1-2 large wetbags. In lieu of a diaper pail and pail liner, some people use large (usually hanging) wetbags. Either option is fine and is totally personal preference.
It's always nice to have a handful of doublers to add extra absorbency in a pinch, but they may not be needed. OPTIONAL
Disposable liners can make solid poop a breeze to flush; however, some older septic systems will clog with disposable liners, so be careful. Fleece liners will add a stay-dry feeling to any diaper that doesn't already have one, and can be used to protect diapers if you have to use a non-cloth diaper safe diaper cream (wash separately with clothes after use). How many? It depends on how often you are going to use them! Disposable liners usually come in large packs that you'll replace as you use them. Fleece liners can be used every diaper change (for instance, if you use prefolds and always want a stay-dry feeling) or rarely, just when you need to use a special diaper cream. So how many you need depends on your anticipated use. OPTIONAL
24-36+ wipes. You're already doing cloth diapers, might as well do wipes too! (But for real: they get so much more off than disposable wipes, and you are far less likely to get poop on you wiping with cloth!) Also: wipe solution. Technically these are optional but I highly recommend making the switch! There are a lot of ways to use these - some people fill a peri bottle with solution, some people have a small spray bottle, some people have container of solution that they keep pre-moistened wipes in. Some people spray the wipes; some people spray the baby's bottom. While on the go, some people will take a baggie of wet wipes and some people will take dry wipes and the spray bottle. Whatever works for you is the right way!
2-3 Snappies. Only needed if using flats, prefolds, or snapless fitteds to secure the diapers. Not needed otherwise. (You could also use old-fashioned diaper pins.) OPTIONAL
Cloth-diaper safe rash cream:
This can be used as a preventative, to make cleaning poop off easier (hint: it doesn't stick as much to the baby!), and to clear up rashes. CJ's BUTTer is a popular option, as is plain coconut oil.
Used to spray off solid poop into the toilet, where it can be flushed. However, you don't need this until your child has started solids at about six months of age. Some people opt to skip the sprayer and instead "swish" or "swirl" their diapers in the toilet (hold the diaper in the water and flush the toilet) or to scrape their diapers (using a designated spatula to scrape the poop into the toilet). Some kids grace their parents with poop that immediately can just be "plopped" into the toilet and no spraying, swishing, or scraping is necessary! OPTIONAL
Cloth-diaper safe detergent:
Don't ruin your diapers! Use a detergent that is safe for cloth diapers.
Somewhere to dry your diapers outside, preferably in the sun. Get out stains and lengthen the life of your diapers! Also: clothespins. OPTIONAL