That’s a nice article. Since I think you are talking about a barrel composter, probably a tumbler, I’ll include this article.
http://www.planetnatural.com/tumbling-composter/
Composting can be as simple or as complicated as you want to make it. If you just pile compostable material (anything that will break down) in a pile it will eventually rot as long as it can get moisture. People in really dry climates have problems with this approach and may actually dig a pit and bury their compostables so it gets enough moisture or water regularly. But with a tumbler you are talking about a more controlled process.
A few things I’ll emphasize. Moisture is important. You want it barely wet enough, not too wet. Most tumblers hold moisture in pretty well so the biggest danger is that you get it soggy and it stays soggy. Not only will that give you lower quality compost but it will stink when the process goes anaerobic. Be careful not to over-water.
Most compostable materials contain both nitrogen (greens) and carbon (browns). You need both for good composting and you need a proper balance, but you don’t need to be extremely precise in this balance. You can’t be anyway. There is no way you are going to know exactly how much nitrogen and how much carbon something contains. Fresh grass clipping still green are considered “greens” because they are higher in nitrogen than carbon. But dried grass clipping are considered “browns” because they contain more carbon than nitrogen. What stage are yours in if you use them? I’ve tried looking at formulas to determine a good mix but you have to do so much guessing to start with it’s pretty hopeless. Just try to go by some of the rules of thumb and let experience be your guide.
One problem you are going to have is that you need to let the stuff work about a month at least for it to become compost but you’ll have stuff to add to it regularly. Getting the mix of greens and browns close, turning it regularly, and getting the moisture right helps speed up the process but it’s quite possible it will take more than a month for it to finish. You need to come up with a way to store the stuff while waiting for that batch to finish. It will be “working” while it’s stored and if it gets out of balanced it can go anaerobic on you and start to smell really badly. I’m out in the country and pile my stuff in a pile to wait. You may want to consider an additional composter for that storage. I don’t know the best way to solve this for you.
Depending on what you add, it’s quite possible not everything will be finished compost when you are ready to use it. Wood breaks down a lot slower than many other things. Peach or plum pits can take forever. I built a frame out of 2x4’s and ½” hardware cloth to strain my finished compost through. It gets out the big stuff and anything that sifts through is called compost. The big chunks get thrown in with the next batch.
I store my finished compost in old plastic chicken feed bags until I’m ready to use it. If you use paper feed bags the stuff will continue to compost and rot the bag. That makes a mess.
Sweet PDZ is good to spread on your yard, especially if you like cutting the grass. Some PDZ itself acts as a fertilizer bringing certain nutrients but the stuff it absorbs gets released gradually and acts as fertilizer. (Different PDZ’s have different make-ups, some being natural and some manmade. Both kinds are good.) It will help the grass grow. I’d use the sand with PDZ to level the yard and fill in low spots. Just rake it in. And don’t worry if some sand or PDZ makes its way into your composter. It won’t hurt it.