I've used various wool covers/soakers over the years. For actual use you do use them just as you would a PUL cover. Mostly they're used at night because they're extremely breathable so they're especially suited for that (plus they tend to be expensive and difficult to care for so using only once per day helps with that). But many use them during the day too, no reason you can't do that... Then when you take it off you just hang it to dry and then use it again once it's dry. Wool covers are 'self-cleaning' to a certain extent so as long as they're not soiled, you only need to wash them once every 1-3 weeks (depending on the age of the child mostly and how concentrated it is, if it's still stinky when dry then it needs washing).
Not sure what kind/style you've received but they generally work over any kind of diaper. If they're scratchy looking then they're probably homemade with store bought wool (or recycled from an old wool sweater). Most babies are apparently not bothered by this but then I've only ever used really soft wool covers (most 'commercial' wool covers are actually extremely buttery soft!).
Washing depends on the kind of wool in question. If it's felted wool you can wash it carefully in the washer. You can tell if it's felted by how tight the knit feels/looks, with felted wool you can barely see the knit at all, it's all shrunk/fused together. If it's not felted then you have to wash by hand (very gently, never wring out for example) with a wool wash or a gentle soap (baby shampoo for example). Every once in a while you'll need to relanolize it (more often if the soap you use has no lanolin, many specialized wool washes have it built-in). The lanolin is part of what makes it waterproof... You can find more detailed instructions online for washing and lanolizing. It's not that difficult but it is a little more time consuming than a PUL cover that you just throw in the machine. Many feel it's well worth the time/effort for your little one to be swaddled in a natural fabric that's sooo breathable...