Most items that you gather out in the world can be taken home and placed on your homestead. Simply click the item in your backpack and click in an open space on your homestead to put it down.
Special homestead decorations can be purchased with both Coins and Bank Notes from the Shop by clicking the purple bag icon on your homestead.
During some of the seasonal events like Frost Fayre, specially themed decorations are released. For instance, during Frost Fayre in 2012 you could purchase Rudolph, The Rocking Reindeer and Candy Cane Boots to place around your homestead. Specially themed items are usually only available to purchase during the part of the year surrounding each major holiday.