Buildings can be accessed by clicking on the Hammer icon towards the top right of your farm
This will open a menu where you can see all the available buildings. Some of them will require you to level your Bumpkin before you can place them.
Once you have the building you wish to place, click on it and you will be taken back to your farm screen.
Areas highlighted in red are not available for anything to be placed, navigate your building into an open space and click the green check mark. There will then be a timer until your new building is available to use.