Here's how you could do that.
You can make calcium carbonate,
#"CaO"_ ((s)) + "H"_ 2"O"_ ((l)) -> "Ca"("OH")_ (2(s))#
The resulting solution of calcium hydroxide is called limewater. Pure limewater is colorless. When limewater contains excess calcium hydroxide, its color changes to mily, which is why you'll see it referred to as milk of lime.
In order to form calcium carbonate, or limestone, you need to pass carbon dioxide through this calcium hydroxide solution. The limewater, which is clear when pure, will turn milky as a result of the formation of the insoluble calcium carbonate
#"Ca"("OH")_ (2(s)) + "CO"_ (2(g)) -> "CaCO"_ (3(s)) darr + "H"_ 2"O"_((l))#
The calcium carbonate will precipitate out of solution, and can then be separated by filtration.
As an interesting fact, heating the calcium carbonate will cause it to undergo decomposition to reform calcium oxide and carbon dioxide
#"CaCO"_ (3(s)) stackrel(color(red)(Delta)color(white)(aa))(->) "CaO"_ ((s)) + "CO"_(2(g))# #uarr#