See the furniture store article for more information on buying furniture. To place furniture in your home, open your housing menu when inside of your home and choose "Furnish".
You will see a list of furniture items that have not been placed yet in the bottom right corner of your screen.
Select which furniture item to place by using arrow keys Up and Down.
Use number pad keys 7 and 9 to move the item to the left and right.
Use number pad keys 8 and 5 to move the item forwards and backwards.
Use number pad keys 4 and 6 to rotate the item.
Use the scroll wheel on your mouse to move an item up and down.
You can increase the speed at which you move items around by pressing Capslock. You can decrease the speed by pressing Shift.
You can press E to snap the furniture item to the ground.
When you are ready to confirm the placement for an item, press Enter then Enter again to confirm.
Then you can continue placing more furniture items or press Backspace to exit.
TIP: You can also place outdoor furniture items around the outside of your house. The process works the same as indoors, except you should open your housing menu when outside of your house.