Does this composting method work?

Read up on it and it seems almost too simple for good composting.
Get 2 plastic garbage cans and drill small holes in them for ventilation. Spend a week putting compost stuff in the one that has compost already in it (the other is empty). At the end of the week, dump the compost can into the other one. Lather, rinse, repeat.

At anytime should I be putting water on it? Compost starter (like alfalfa)? Does it theoretically work but is highly inefficient?

If you’re not using the right mix of composting materials (carbon-nitrogen ratio, and nothing in there which shouldn’t be), it won’t work well, and neither will other methods.

As you’d always be adding new material, you’re never going to get to fully finished compost – that is, part of what’s in the can will get there, but other parts won’t be, and I don’t see how that method’s going to let you separate them. Are you sure you didn’t misunderstand instructions telling you to fill one can, then leave that one while you fill the other, then use the contents of the first one and start over? Or to have two sets of cans, with the weekly dumping being meant to substitute for turning the pile?

Whether you need to add water depends on how wet it is; which is going to depend both on the moisture content of what you put in the can, and the outside humidity (and, if you don’t have the lid on, whether it rains.)

There’s also the question of what you’re aiming for. Aiming for something that got hot enough for long enough to kill pathogens, aiming for something that won’t stink too much until you can till it into your garden, and aiming for something you can use in a potting soil mix aren’t the same thing.

I know this was part of it

Composting can be tricky, most newcomers keep it too wet and too much nitrogen. I always kept mine on the ls

slight dry side and used lots of carbon, for a good starter I would dump my material out on bare ground and go over it with the lawnmower. It got a lot of dirt on it which seemed to kick it off real fast.