Bone have some special cells.
There's "osteoblasts" which "build" bones, and "osteoclasts" which "crash" bones and break them down.
You might have heard that drinking milk builds strong bones, that's because they're talking about the calcium. Calcium is used to build bones, which is what the osteoblasts do. When the osteoclasts break down bones, that calcium ends up in the bloodstream.
Anyways, all you need to know is that parathyroid hormone increases calcium in the blood, and calcitonin reduces calcium in the blood. You can kinda see it in the name: "calcitonin" tones down calcium.
This is done by changing the ratio of osteoblasts:osteoclasts.
To increase calcium levels, parathyroid hormone would result in increased osteoclasts and decreased osteoblasts.
To tone down calcium, calcitonin would result in increased osteoblasts and decreased osteoclasts.
Hope this helps :)